We are both unemployed: I'm freelancing making very little money and she is on unemployment looking for work after just graduating with her Masters degree.
My girlfiend is a volunteer Board member at a non-profit. Its been great for her as she has met many people that she feels can benefit her career wise. I have been to the events and met most of the people she volunteers with.

(OVER THE COURSE OF 5 DAYS):
About two months ago she told me she wanted to break up. We had been fighting a lot and she told me that she hadn't experienced enough in her life and that she needed time to "figure herself out". She wanted me to leave or for us to make arrangements right away. She spoke about using the time to become a better girlfriend for me and about how people break up and reconnect after years all the time. She said that, that is what she wanted. I told her that I could not make any promises about having a future but that I loved her enough to let her go.

I was staying at a hotel for two days and during that time we had been speaking on the phone, crying together. She was telling me that she felt that it was the wrong choice and that she would regret it but needed to make it.
Honestly, it felt like she was pushing me to say " I will get back together with you some day". I didn't promise this but I did assure her that we would both be OK.

NOW IT GETS TRICKY
I found a sublet and accepted it on the morning of my third day away from home. I went to the house to pick up my clothes around noon and was with love and affection. She urged me to cancel the sublet and to stay living with her to work it out. After an afternoon of crying together I canceled the sublet. I left for the gym around 4 PM and got text from her saying "Im sorry but I really can't do this, I know I said I wanted to be with you but when you are away its clearer to me".

I was now back at the hotel having lost out on the sublet. She called me about at 2 o clock in the morning drunk. She told me that she loved me and that she missed me and was sorry for being crazy and going back and forth with me. She told me that she was going home to sleep and wanted me to come back in the morning to REALLY work things out.

I went back in the morning and as it turns out, she told me that after she spoke to me at 2am she went to another part of town to hang out with one of the guys that volunteers at the non-profit with her. She said that they didn't have sex but did other things.

To make a long story a little shorter:
- I forgave her after a day of crying and two more Indecision about our relationship from her part.
- I emailed the guy and told him that this can never happen again.
- she told me it wouldn't happen again and I actually do trust her
- we are back together; still fighting but working on it and getting better

AT THIS POINT:
She still volunteers at the organization along with the guy. The organization has social events and I am upset that they see each other even though nothing happens and they are not alone together. I haven't asked her to quit because I feel that it is too selfish but I don't think I can bear that they still see each other.
I don't want to hold a grudge and end up punishing her later.

Should I ask her to quit?
WHAT SHOULD I DO?

So in essence nothing has changed,you jumped right back on the roundabout and accepted the terms of 'we'll work it out' but nothing has changed.

She broke the trust in your relationship by 'doing other things,but not sex' with a guy she is still in contact with,and yo uhave accepted it because you don't want her to feel bad...

But what's she doing to show you she means business this time.

Unless she found herself in the 5 days,she is going to want find herself again.

I wonder,why she 'did things' with this other guy, when you were just at the end of the phone?

I don't mean to offend,but she sounds very immature.

On the break you had a plan,and a good one,the relationship was not working,but she drew you back in again,you let her,and still nothing is resolved,the same problems are there.

Either address the problems,or walk away.

The relationship sounds mentally and emotionally draining.

Well, can you see yourself getting over this? Granted, she still wants out... I feel that she wanted out due to this guy. It can't be that this guy and her just went from "Hi, we're friends..." straight to "we did stuff." So in my assumptions, they must have flirted while working and such, and that led to her being confused about the relationship between you two, and thus, she ended things with you. Her asking for a "break" was just her asking about a "breakup" to see how things went with the other guy.

In all honesty, I think you should leave her, let her make up her mind (REALLY make up her mind), which will take some time (few weeks to a few months) and let her figure things out.

I know that's rough on your living situation, not to mention finances, so perhaps at this point, finding another sublet or maybe crashing at a friend's place for a little may be a good idea. She'll call you and tell you to come back, then make you leave, then come back, and in all honesty, this is not fair for you. Even though it's hard, I suggest you let her be, let her figure things out on her own, and when she does, you'll have a better picture as to what's going on.

What's all the fighting about? What are the issues your working on?

For whatever reason things didn't work out with the other guy, she still had you waiting in the wings, so she has lost nothing at all. But you have been jerked back, and forth, like a yo yo!

Making her quit volunteering may stroke your ego and ease your distrust, and insecurity, but I think it makes more problems than it solves and think you should have given getting back together a lot more thought. Based on facts and not just feelings.

I still think, depending on what issues you continue to fight about, you give staying in the relationship a lot more thought than you had before, because you're really not solving anything, or working together well at all.

Lack of finances will do that, cause a lot of strain, on an already fragile relationship. But the cheating would make me rethink this whole situation.