Hello
Gyp 
and welcome!
I picked up on the word "(finally)" in your post. I'll just bet you, like the rest of us here, could tell many stories of the journey you have shared with this 32-year-old daughter of yours.
Indeed there is much to be thankful for if she is about to begin DBT. Even agreeing to embark in it is a biggie.

So many stay in denial...
"I'm not the problem...your are!"...is something that is heard a lot.
It is encouraging, too, that you have heard a psychologist tell you that she can heal and have a functional life...very encouraging!
For sure there is a lot of work ahead for her and her perseverance is going to be key...but there is also work ahead for you. Have you ever had counselling for yourself...spoken to a professional about how to better deal with her BPD behaviours? Have you read any books on the illness? Tons of information is on this website with links to more.
We all live with hope for better futures with these troubled loved ones of ours but it is best not to try to set up a future that YOU want it to be...then have great disappointment when things turn out differently.
Once again, welcome. Hope you become more and more comfortable in sharing in this forum as things go forward with your daughter. We really do learn from each other here...what is working...what isn't working. Mainly it is feeling the support we get from others as we make changes in ourselves.
Huat