Hi Capt... .I think we can all appreciate where you are at the moment. It was definitely an AHA moment when I found out about BPD. As with you, as I read the stories of others I felt they knew exactly what I was going through. Firstly find some comfort in the fact that you are not alone and also that your partner is also not alone. It is a hard and rough road to stay and support your pwBPD. I have found the lessons here very worthwhile - not to read just once but to revisit again and again. There is no secret answer on how to cope and survive but there is lots of support.
Take care of you and the children - I know my 2 have been perplexed by the behaviour of their step-father and I am very careful how I explain it to them (they are 12 and 14 so able to start to comprehend concepts of depression and anxiety etc).
Read lots and post whenever you need to.