Your requests are pretty sensible, although part 4 (treatment) is a tough one. She may be reluctant. She may fail to find treatment that works for her or decide to leave it for her own reasons (good or bad) months into a program, after coming back.
It sounds like she's met the other three requirements already.
I'm also confused about your situation and what you want. (Pardon me if this was all in older posts; I didn't go looking)
Are you dating anybody else yet? (She said something about that in her txt)
Are they your kids, or hers? Are you still in contact with them? What sort of relationship did you have with the kids when you were together?
What sort of "start over" do you want?
- Being in contact as friends?
- A romantic/sexual r/s?
- Living together?
- Parenting together?
- All of the above?
I've got a few recommendations:
- Don't discuss resuming your r/s with her by text / email. Any discussions like this are best done face to face, with telephone as a second choice.
- Take things slowly; don't jump back together as if nothing had happened.
- Read this from the Lessons here on the Staying Boards Tools: The Do's and Don'ts for a BPD relationship