Well, she came back to the house one day after moving out and saw messages between me and a girl on the dating site, with me complaining about my boring marriage. She of course freaked out. I apologized and begged her to please keep working on things.
You should not have "apologized and begged her to please keep working on things", what she did was far worse than what you were doing. Did she "apologized and begged YOU to please keep working on things" as well? Why is it ok for her to cheat and get away with it but not you? Do you not see the double standard?
But shortly thereafter she started staying with the emotional affair guy, but according to her, no sex.
Assume this is a lie, they never tell the truth until you pull out video evidence of it. There's no way she would admit to sex because it would knock her off her high horse.
When I found this out I told her we were done. She then begged me to take her back, as she didn't love him, she loved me. So I did with conditions of no more dating sites, not more OM, and continuing marriage therapy. That was two weeks ago.
Remember this, when you want to end things she wants to keep you but as soon as you give in and say you will work on it she pulls away.
Last night at our marriage counseling session, she said she still loves me, but she isn't happy. Naively I thought things were getting better. When the therapist and I asked her what she wanted, she said she didn't know. But she started talking in terms of "if were to separate would we still blah blah blah." I was like, I'm not even thinking of that. She says she can't get over my messages to the dating site girl, and that she doesn't trust me. And that she feels confined in our marriage.
She wants to separate and this is her way of setting the stage so you are not taken by surprise when she leaves again.
So now I don't know what to do. I have patience, but I don't think she really wants to be married anymore. And most of my friends feel as if she doesn't want to be either. More like she wants the marriage over but doesn't want to be the bad guy and end it.
Your friends are correct.
So do you just sit around like a sap and let her humiliate you again or beat her to the punch and save some of your dignity.
She wants out but on HER terms. If you kick her to the curb she will most likely beg to stay again. If it were me, I would tell her I wasn't happy and didn't want to stay with someone who didn't want to be with me or doesn't honor their commitments so GTFO. When she tries to talk you out of it tell her too bad, she already made those promises before and went back on them so not again. Remember this is HER fault, not yours. She needs to do all the begging and pleading.
Once she has had a couple of months by herself to think about things then maybe open communications again. She needs to really understand how life without you is going to feel (we don't know what we got until its gone) and if she asks you about doing the online dating again tell her you can't make any promises.