Thanks for all the replies everyone! Ladyfriend (i'll refer to her as M) and I had a looong talk today, about a bit of everything going on.
First of all though, a few clarifications about what happened, and the events that lead up to it.
M has been at an intense training session for the past 6 weeks (15 hour days, different state, slow to make friends). We have been having issues between us for probably close to a year now, stemming primarily from her absent sex drive. This doesn't excuse anything, but its important for understanding I think. The last day of her institute, Friday, she went out and slept with this guy (who I will refer to as D- for douchenozzle) she had become friends with while there. Saturday morning she called me, confessed, apologized, and was remorseful.
I do genuinely think she is sorry, but that doesn't justify anything in my mind. It does obviously open up the road to forgiveness though. I do think I have it in me to forgive, I love this girl, a lot. The strongest barrier to our relationship is re-establishing trust and me believing that she won't cheat again.
She has not had anymore contact with D since. She has told me she has no intention of pursuing anything beyond friendship with him. However the thought of her with him is, unsettling, to me. So I asked her to cut him out of her life. A pretty strong reaction, I'll admit, but its important to me that she can choose me over him (which feels childish). Since he is a core part of her new group of friends, she claims this would mean her not seeing the entire group. I feel bad about this, but I have anxiety at just the thought of her hanging out with him. She has been very resistant to this demand, but has finally said she will comply with it. I don't know if this is the right thing for me to do.
Poly related things
M still says she is interested in Poly, not with D, and that this was just all poor timing. I still don't know if I could handle it, but I'm honestly not even sure what Poly is. Or the distinction between poly and swingers and stuff. I could handle 3somes, and that is something else we have talked about and are open to trying. Is that something that can lead to poly?