Welcome and hello

Great that you were able to do a collaborative divorce, and that your kids have had some therapy.

son has talked about ending his life.
Oof. That is tough. My son talked about ending his life starting at age 8 and I have never felt so helpless. I made a lot of mistakes responding to him until he was 11 or 12, which is when I learned to validate his feelings (so counter-intuitive... .). "You must feel so sad to say that. Did something happen today that you want to talk about?" Emotional validation is a skill taught by psychologists who noticed that reassuring people with suicidal ideation that they are wonderful only made them more suicidal
If I could do that SI period over again with my son (who is now 16), I would've done family counseling together with him. He and I had individual counseling, but we really needed some family counseling, too. A skilled psychologist (S16's individual T) helped us work through some complicated dynamics and once we did that, we had shared language for the many hours outside of therapy. My T was also helpful, although I do think it helps to have a child psychologist specifically involved when the issue is a child's mental health struggles.
It can be very emotionally isolating to live in a home with BPD + codependent dynamics, especially for kids.
There is also a wonderful book by Bill Eddy called Don't Alienate the Kids, about raising emotionally resilient kids when one parent has BPD. It is really about modeling the kinds of behaviors needed to cope with a BPD loved one, which will ideally strengthen the bond between you and your kids while giving them some coping skills.
I keep telling them that I can only control my behavior. I generally do not give in to the temptation of saying what I really think about mom to them, though I do find myself slipping up occasionally... . I've given the kids express permission to call me out if they feel I'm bad mouthing mom, and they've done it at times.
I understand this, and can see how hard you are working to be fair. One thing that might help with this -- focusing on mom's behavior and not on mom's personality. "I can't control what mom does, but let's talk about some behaviors that we all know are hard to deal with. I found certain behaviors of hers challenging to cope with as an adult. As kids, this is going to be extra tough for you guys. The good news, there are skills. The bad news, they aren't easy -- altho they'll make a huge difference in your life going forward. I'm even thinking we go talk to the therapist together and try to come up with some exercises for when mom says x and y and z, so we can figure out a safe way for you guys to respond." Then practice the skills with them, starting with strangers, then working up to more difficult people.
If you aren't comfortable saying that mom has BPD (understandable), it might be helpful for you to read books about dealing with a BPD loved one, if you haven't already. Books like Loving Someone with BPD by Shari Manning and Overcoming BPD by Valerie Porr are very compassionate about BPD loved ones (while being very firm about boundaries), which can be tough for people who are still healing from bad BPD behaviors.
If you want to read books that are a bit less empathetic, there are others.
The main thing is to focus on validating how your kids feel, and curbing impulses to solve or fix or save or rescue them.
My favorite book throughout all of this is I Don't Have to Make Everything All Better by the Lundstroms. They suggest validating questions because the validation coupled with questions gives the other person a sense of responsibility, which leads to competence.
People with BPD have a higher than normal need for validation and an abysmal ability to validate others, so you kids will be extra thirsty. You'll have to provide double the validation until they reach a point where they can start to self-validate, which may take a couple of years or longer.
The key, I believe, is to recognize how emotionally lonely it is when one parent has BPD and to do what you can to create emotional closeness. Fortunately, your kids are alert to mom's behavior so you have lots of room to help them skill up.
