A few thoughts...
Why did you push her away six months ago? What was so horrible between you two?
If you do agree to poly:
- you can ask for things to move slowly;
- you don't have to come home to find them on the couch. You can establish boundaries that make your home or specific rooms off-limits;
- don't think that just because she wants this, that it means she will jump into bed with this guy right away. This is the time to sit down and negotiate what is comfortable for both of you;
- be sure to discuss safer sex practices; and
- you wouldn't get "half of her." That's nonsense. Are you ever half a person? She is a whole person wherever she goes. Of course, if you feel her attention is elsewhere, you can speak up and tell her.