Despair sounds like a pretty natural response to everything that's going on for you right now. It doesn't make you 'weak' or less of a person to feel horrible about being away from your kids, having had your DH cheat on you, and possibly having your kids at the house of the woman he cheated with! You have every right to do a little grieving and railing against the situation.
What can you do right now to take care of yourself? You sound burned out and, frankly, depressed. Is the intensity of what you're feeling recent, or has it been going on for a long time? The reason I ask is that you may need some outside help to overcome some of your despair if it has been going on for awhile. Your adrenals are probably shot from all the stress you've gone through, if nothing else. Is it possible for you to get some naturopathic care, or counseling, or acupuncture, or even just a day at the spa?
I've been there (recently) mama. Sometimes I feel like handing over my daughter and throwing in the proverbial towel. Sometimes I really regret the decision to have her, and then feel even worse, racked by mother guilt. But thoughts like that are just expressions of the desire to escape a really bad situation with her dad, and extreme exhaustion, kwim?
Do you have friends and/or relatives who can be with you right now? Anxiety is exacerbated by isolation, so even if you can just talk to someone on the phone or go out for coffee for a little while might help in the short-term.
The intensity will pass, mama. Not as quickly as you'd like, to be sure. But you will survive this time and look back on it and wonder how you ever made it through. You sound like a very strong and capable woman, who is also human. You can't really ask more of yourself than that.