How to handle the story that my uBPDw tells my kids?

[Depression = 72% of members]

Background: I am in a decade and a half relationship with my uBPDw, have two kids in elementary school. I moved on to rent an APARTMENT when I was forced out of home around five months back (it happened twice years back, during which I returned home after a week. But this time, I decided to not go back). Since then, I visit HOME every evening to spend time with my kids and they are with me at the APARTMENT over the weekends. My wife and I are on talking terms most of the days. We are not intimate any more (her decision). It is fine by me as I am working on establishing new boundaries. I am not for divorce at this time considering the kids, while I am open to it if the situation gets worse. She does only some part time work from home, it is a consideration for me not going for divorce at this time (though she would say during arguments that we should divorce). 
Here is my current issue:
In her mind, she theorizes that I moved out to an apartment to engage more with my family [who, ironically, don't even live in the same country]. During bad days, she keeps repeating it to my kids and says that I would abandon them (kids) and they would all be in the streets (though I have told her that she would keep the home). She doesn't have any cognizance of how her actions and forcing me out created this situation. To keep daily peace, I have not spoken to her about it. While I don't worry about what she thinks/says, I worry about the impact it has on my kids (my younger one last week just parroted her talk of how he is not part of 'my family').
Question #1: What do I do in this situation? At the minimum, I think I can refute in a positive way her theory of me "moving out for my family". Without assigning blame, I have mentioned to her how positive this two home setup has been as it has reduced conflict and given her space. Do you think talking to her about how her actions caused the situation will help? OR, do I continue to focus on the positives of the two home setup? At some level, I feel REPETITION is key - I feel I need to repeat my story (of how better the two home setup is for the family) to counter her entrenching her story (that I am doing it for my family and that I would abandon the kids).
Question #2: I realize that I need to talk to my older one (when he is with me) about how he feels about all this (I am focusing on the older one, as younger one is not the age to have a conversation). He calls it 'the problem' and sometimes would ask me to solve it. I didn't have a good answer for him. What do I talk to him about? Should I ask him if he really thinks that I would leave him - and assure him? He too was forced out with me this time, but went back home in a week's time. To avoid pulling at two ends, I don't talk to him any ill of my wife and focus on other things. But I learnt to need to validate their feelings - so, I don't do "but, mommy loves you" any more. I am learning and I have a long way to go in this aspect.
Please advise. Thank you!

[healthfreedom4s]

Background: I am in a decade and a half relationship with my uBPDw, have two kids in elementary school. I moved on to rent an APARTMENT when I was forced out of home around five months back (it happened twice years back, during which I returned home after a week. But this time, I decided to not go back). Since then, I visit HOME every evening to spend time with my kids and they are with me at the APARTMENT over the weekends. My wife and I are on talking terms most of the days. We are not intimate any more (her decision). It is fine by me as I am working on establishing new boundaries. I am not for divorce at this time considering the kids, while I am open to it if the situation gets worse. She does only some part time work from home, it is a consideration for me not going for divorce at this time (though she would say during arguments that we should divorce). 
Here is my current issue:
In her mind, she theorizes that I moved out to an apartment to engage more with my family [who, ironically, don't even live in the same country]. During bad days, she keeps repeating it to my kids and says that I would abandon them (kids) and they would all be in the streets (though I have told her that she would keep the home). She doesn't have any cognizance of how her actions and forcing me out created this situation. To keep daily peace, I have not spoken to her about it. While I don't worry about what she thinks/says, I worry about the impact it has on my kids (my younger one last week just parroted her talk of how he is not part of 'my family').
Question #1: What do I do in this situation? At the minimum, I think I can refute in a positive way her theory of me "moving out for my family". Without assigning blame, I have mentioned to her how positive this two home setup has been as it has reduced conflict and given her space. Do you think talking to her about how her actions caused the situation will help? OR, do I continue to focus on the positives of the two home setup? At some level, I feel REPETITION is key - I feel I need to repeat my story (of how better the two home setup is for the family) to counter her entrenching her story (that I am doing it for my family and that I would abandon the kids).
Question #2: I realize that I need to talk to my older one (when he is with me) about how he feels about all this (I am focusing on the older one, as younger one is not the age to have a conversation). He calls it 'the problem' and sometimes would ask me to solve it. I didn't have a good answer for him. What do I talk to him about? Should I ask him if he really thinks that I would leave him - and assure him? He too was forced out with me this time, but went back home in a week's time. To avoid pulling at two ends, I don't talk to him any ill of my wife and focus on other things. But I learnt to need to validate their feelings - so, I don't do "but, mommy loves you" any more. I am learning and I have a long way to go in this aspect.
Please advise. Thank you!

[RELATIONSHIP PROBLEM SOLVING]

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[PeteWitsend]

...
Question #1: What do I do in this situation? At the minimum, I think I can refute in a positive way her theory of me "moving out for my family". Without assigning blame, I have mentioned to her how positive this two home setup has been as it has reduced conflict and given her space. Do you think talking to her about how her actions caused the situation will help? OR, do I continue to focus on the positives of the two home setup? At some level, I feel REPETITION is key - I feel I need to repeat my story (of how better the two home setup is for the family) to counter her entrenching her story (that I am doing it for my family and that I would abandon the kids).

What I've been advised is to say something along the lines of "that's your mom's opinion; I don't agree for these reasons."

And then, this is key: Ask your kid(s) what THEY believe and listen to their concerns.

I was in a similar situation; my daughter said "Mama said you abandoned us because you didn't want a family."  I told her that wasn't true, I stayed close by because I loved her and wanted to be involved in her life, but I couldn't stay married to her mom because we didn't get along.  She said something like "Now I don't know who to believe" but I said she didn't have to believe either of us, she was free to make up her own mind, but I'd always stay nearby and would always be her father. 

I took a similar approach when BPDxw said awful things to her about my FOO; told her I didn't agree with her mom's opinions, and asked D what she believed and why. 

This advice was validated by my D's therapist, BTW.  He said kids know more than we think, and are only looking to you to help them navigate the lies they're getting.  It's important to let them make up their own minds, and if they see one parent not making sense, or telling them stories that contradict their own lived experience, that parent will lose credibility with them.

Question #2: I realize that I need to talk to my older one (when he is with me) about how he feels about all this (I am focusing on the older one, as younger one is not the age to have a conversation). He calls it 'the problem' and sometimes would ask me to solve it. I didn't have a good answer for him. What do I talk to him about? Should I ask him if he really thinks that I would leave him - and assure him? ...

Yes, absolutely.

And I'll add you shouldn't take some of this stuff lying down.  If this all gets ugly and moves to a divorce, you should have all this documented, and be prepared to fight back, and show your wife has a pattern of attempting to alienate the kids from you. 

Staying separate from a BPDer without the clear legal and financial boundaries of a divorce is playing with fire... you could get burned here.

[healthfreedom4s]

What I've been advised is to say something along the lines of "that's your mom's opinion; I don't agree for these reasons."
And then, this is key: Ask your kid(s) what THEY believe and listen to their concerns.

Hello PeteWitsend,
I have started using your advice of gently refuting uBPDw's opinions with my kid and asking what he thinks. Thank you for your valuable inputs.

Staying separate from a BPDer without the clear legal and financial boundaries of a divorce is playing with fire... you could get burned here.

Thank you for pointing out this risk. Forever Dad did too. Given my cultural conditioning, I am not naturally inclined to a divorce and I am not there yet. I know it is risky. The two home setup is a low conflict arrangement at this time, but I know things can change very quickly with a BPD partner. I want to give this arrangement sometime, before moving towards divorce. 

Thank you again for your advice!