Do I give "us" another shot?

I was dating a girl for four years, I'm 36 she's 29, the last 6 to 8 months we grew apart and there was doubt that we both loved and wanted to be with each other. Two years into that relationship we got a place together, the beginning of July I decided but it wasn't healthy for us to live together anymore, so I broke it off and we moved out of the apartment. Within the last 4 to 5 months we kept in contact (mostly texts and phone calls) and we saw each other when time allows, 2 to 4 times a month with loving actions being done in those visits. She wanted to get back together, as did I... but I believe we just needed this "time" to figure ourselves and our relationship out… the hope that our issues could be resolved and we could find ourselves so we could be better together, and with the hope of us getting back together. We never said we were "done" just needed some time and like I said we seen each other, admitted that we missed each other, and did what loving people do, if you know what I mean. Now here’s my dilemma, always thought it was a mutual love and my intention is to get back together, and I believe it to be so. So three weeks ago we went to church, and I'm Catholic, she wanted to come with me and during the sign of peace we shared a kiss, we did this when we were dating. Which is I believe a sign of love. We later went to brunch and a walk in the park and talked about our situation\relationship. She admitted that she went on a date Wednesday, but she couldn’t stop thinking of me and felt sick. I hurt a little that she went on the date, but felt awesome that nothing more came of it. I’ve not seen anyone or been with anyone either, I’m just not ready for that yet. I came away feeling like a lot of progression was made and we were just about if not there to be a couple again. The day after, Monday she went through her emails from our relationship and sent me some very loving reminders of how awesome we were together, again thinking that we were there.
So 2 1/2 weeks later and my dilemma, she said she seeing somebody and hooking up. I don't know what to do or feel. The following day I sent her a poem asking where I stand. Her response is I want to be with you so bad. I asked her can you still? And her response was I can do anything I want, with a ':-)'. I told her than that we seriously have some talking to do, and she agreed. So we are going to talk tonight, but I don't know what to do. I love her, but it hurts that she did that.
We're not "together" so she believes she did nothing wrong and I really can't hold any fault. But taking in consideration the last four years and the last five months of our separation we never said we were done, never ended on bad terms, admitted we still loved each other and wanted to be with each other. So I'm having a hard time justifying what she did and why. Do I move on?