I agree with many of the others, if she wants to be on her own, have her space, then make sure that she has her space. Including financially.
(The only exception is that if your name is actually on the lease, then you may be liable for that.)
If you are not legally entangled (lease, electric bill, etc.) then simply say that you are willing to give her her space and that includes the financial aspect.
It's call boundaries brother. You can't make her do anything, but you can be clear on what you will do and not do.
For example, if I cannot live in the apartment, I will not pay for any of it's costs.
If you want to date other men and go dancing with them, I do not wish to continue a relationship with you.
You can tell her what you want. If you love her, then say I love you, and would like to have an exclusive relationship with you. However, if she is not willing to do that, then you are willing to set her free.
Being needy is the wrong approach. So just go on with your life, hang out with the guys, volunteer to help with kids or do whatever floats your boat. (Other than dating for a while.) See what happens. If she really wants you, she will come back, if not, then you have your answer and can consider yourself lucky to learn this before you got married, had kids and have to give her 1/2 the stuff you accumulate plus pay child support and get to see your kid maybe 3 or 4 days every two weeks.
I wouldn't be mean about any of this, rather be matter of fact. Let her know you love her and that the choice is hers. Let her know that you will not share her with others and the choice is hers.
The key is to do this without anger, bitterness or being hurt and needy.
Needy is not attractive.
Strong and in control is attractive.
If you don't attract her back, then what you've learned will help in the next relationship.
I can understand your hurt. My wife left me for a 52 year old married man. It hurt for about the first year. I'm still a bit angry about it. But when I look back, it's one of the best things to happen to me.
But it was also one of the worst things to happen to me, and I had to go through the worst first to get to the best part.
You can't decide for her, you can't coerce, cajole or convince her. You simply have to be the best man you can be, and let the chips fall where they may.
That's the best advice I have to offer my CEG brother. Use what you find helpful and leave the rest.
TB