Hello Malibu
What a difficult situation you are finding yourself in. Kuddos to you, you seem to be a safe haven for your children.
How wonderful you are taking their emotional situation seriously. They are lucky.
I think your comparison with the broken car can be good, althought it can come across as very drastic, and unchangeable. Maybe you can add that everyone has something that is a bit odd. I think it is also superimportant to tell your children that none of the behaviors of their mother is their fault. Children tend to take the blame for everything (they feel they are the center of the world, so how can anything not be their fault). And of course for children of BPD this is even more outspoken (it was so for me, too - my mum is BPD).
The dad of my daughter is autistic. I have worried a lot about that, and about the impact it might have on her wellbeing. Recently however I have noticed I have gotten some more breathing space. My T has told me that no matter what happens to a child, the most important thing is that it knows it's not alone, that someone is there to listen. This someone here is you. If you can guarantee to be this safe haven for your children, and to always listen to them and take them seriously, I think a lot of damage can be prevented.
Also, do you think it would be a good idea to let them speak to a child psychologist ? Even if it is just one or a few conversations, from time to time, just to check up on them ? When I have an issue to deal with regarding my daughter and I don't know how to handle it, I ask a psychologist. My child does not go to one herself, but I do ask the opinion of a professional when dealing with the 'serious stuff' (autism/BPD).
She is depressed, so I've talked about that and the need to be sensitive because her heart is broken
What do you mean with 'the need to be sensitive' ? I would think it's important to watch out to not make your children walk on eggshells around mum. Telling them her heart is broken sounds very serious for a child, and it might result in them wanting to protect their mother. And that's not their task.
I think it can be important to not picture their mother as a pathetic nutcase, but as someone who, however troubled, is an adult, and able to take responsibility.
When speaking about my BPD mother to my child, I always tell her that grandma has something that is not wired correctly, and that it's very difficult yet not impossible for her to change. And that if she doesn't, this is entirely her responsibility. We sometimes make a drawing : we draw grandma, and we draw my child. And we make sure the picture reflects very well that it's two different persons. Or we draw two boxes. The one box contains the problems of grandma. Some things out of grandma's box want to go into the box of my daughter. But it cannot : my daughter has her own box. So the things go back into grandma's box.
This I think is related with having boundaries. I never learned that it was ok to have them. Having a BPD mum made sure I didn't. So it was something I had to work on as an adult. And I now realize it is very important that I teach my child to have them, too. So when I notice toxic behavior going her way, I tell her that she can think/say something in the line of 'I am sorry, but this is not my problem, it is yours to deal with.' Also here, we make the box analogy. Of course it's difficult to practise this regarding the behaviors of the mother of your children. After all it's their mum. So I bet it's difficult for you to know how to handle this. Maybe you can practise with behaviors of other children. Like when your children have stories from school friends who do things they don't like. You could make a drawing about it. The possibilities are endless. You can visualise it with real boxes, ... .
Please keep talking to your children, you are doing a great job. If only more dads did this !