Hi Mischa,
Welcome and hello

Impulsive behavior is pretty common to BPD, and not thinking things thru. It sounds like he has projected a full fantasy onto this woman without knowing her. It may not last, hard to say, tho meanwhile you are in a painful position of wait and see. Your kids must feel shattered too, watching their dad abandon the family this way.
What is it like when the two of you communicate right now?
There is no magic formula to fix a relationship on the rocks tho we can share with you skills to mitigate things and prevent them from making things worse.
We're here to lean on if you need support.
LnL