After no communication for months, I reached out to apologize for being unsympathetic (this is before I discovered BPD family

She responded within an hour to my apology and stated she didn't have a problem with me or my husband, but with our daughter... .
This is a comment about BPD, not who is right/wrong in this situation

... .
Both you and your daughter invalidated her (unitentionally or subconsciously) and she reacted to it.
She took your apology as being sincere. I suspect it is... .you're here

She took D efforts as insincere. pwBPD can often read others like a book and she is probably reading the your daughters mixed feelings.
pwBPD are impulsive, as you have seen. They can flip back when things seem settled - as she did with you.
So... .
She didn't feel you all embraced her enough in the beginning. Let's face it, most partners feel that (or worry about that) from the in-laws. A person with BPD can be mortally wounded by this.
I suspect that if your daughter makes amends with no pressure on BPDgf to be reciprocal, gives her time, the wound would heal.
I also suspect that if you go above and beyond being inclusive now (but don't flood it of be fake) that she will come around.
What do you think about that?