Just learned of cheating partner who i suspect is BPD

Just here to see how others may react to this or if this is normal BPD behavior.

I work away from home for a month at a time. This last time I was away when i got back my partner made a comment to the kids along the lines of “remember what I told you not to tell daddy about”. That was obviously a red flag but i didn’t probe. Just took a mental note.

Fast forward a month, my 8 year old daughter spilt the beans, a guy who my partner had gotten together with while we were separated for a year, apparently had slept at the house the day before I came back from work and she saw them kissing, these are the two secrets my daughter was told to keep from me by her my mother.

Is blatant cheating in front of kids a normal female BPD thing to do?

And how would you handle the situation?