Hi Tara,
Is he in therapy yet for his BPD? If not this would be a very good idea to find a therapist who specialises in DBT therapy and has experience with BPD.
If he really wants to change then he needs to try as hard as he can to use his logical thoughts i.e. his brain rather than his emotions. This is not remotely easy to do and can leave the person with BPD feeling quite drained and empty but it does help in the long run - I have BPD myself so talk from experience.
Regarding you coping and not making things more difficult for yourself, you need to set boundaries in both directions. So what I mean is, if he does something which is relatively harmless and isn't going to be a long term issue, for example you want to take the kids somewhere with him at the weekend and he doesn't feel like doing it, just go along with it and try and ask him what he would like to do with them etc. Basically any trivial things that might trigger him it might be best for now to just go along with them as it will make your life easier. The accusations of cheating etc, that is not acceptable. My only idea on this would be, albeit not healthy but offer him your phone for the day... show you have nothing to hide, maybe don't embarrass him by making it so blunt - as this could trigger him, but leave it around 'accidentally' so if he needs to validate his thoughts he can. (I understand all this is exhausting and yes BPD is a pain in the...)
Does his mum know that he has BPD? Family and support for you is critical, you need a healthy balance away from the kids and him which is your time to relax and recharge - I imagine you don't get a lot of that working and having 4 children?
He needs to understand that his emotions are completely irrational and not normal at all. I have had similar thoughts at times, I think we all do from time to time not even just people with BPD, the difference is the emotional response from someone with BPD is so extreme it sparks irrational thoughts and responses because our coping mechanism isn't there like it is in a normal healthy person.
There is an exercise that I did a few months ago which I found quite helpful, it almost sounds stupid when you think about it but remember when someone with BPD is in an emotional 'crisis' it is like talking to a 5 year old, you literally have to spell things out to them.
Anyway the exercise was to draw a straight line with arrows pointing in opposite directions, under one arrow write 'all good' under the other arrow write 'all bad', the task is to write down every day things that happen in his life which he thinks rationally fit under one or the other. The answer is the only things that fit under one or the other are things which are extreme. Most things are a mixture of both, one of the issues with BPD is you normally either see you partner as all good or all bad. Which of course is nonsense. But I read a few articles which actually said that a BPD person when in one of these states almost comes across like they have mild amnesia, like the brain forgets anything good in the moment and exclusively focuses on the bad.
Few other things, when he is feeling overly down, nothing can compare to the power of laughter, it can really help pull someone out of a slump, like anyone with or without a personality disorder.
Lastly he has to want to change, there is a book you can find here
www.connectdurham.altervista.org/CD/documents/BPDWorkbook.pdfwhich I found useful, its more for him than you.
Hope some of that is helpful.
