/what/ - ...

This is a long rambling one so I apologize in advance, I just have no one to talk to and I'm kinda having a really hard time. (and I don't know how to format on this site)

In the last 38 days my wife has stayed home after work 6 times and is never home before midnight. She sometimes doesn't come home at all, staying with a friend and going to work the next morning. This is just what I have been writing down however, as she has been going out a minimum of 3 nights a week (4-5 on average) for about a year now. I have spoken to her multiple times and she claims to just want to have friends and a social life and since she is the primary bread winner she should be able to do what she wants. Note that she is the main earner in the household because she asked me to take less hours to be able to watch our 6 children since childcare is outrageously expensive. 4 are technically my step children but the only steps in my house lead to the second floor; they are all mine and my reason to live. I am their primary caregiver as she is either absent or sleeping or busy. So much so that they have now started asking her why she is always gone or busy or why I don't get to go hang out like she does. She doesn't see the problem and actually gets mad at them for questioning her. Her compromise is to wait until I'm laying them down for bed to go out (where as before she would come home, change and leave) but, she spends the hour prior to that getting ready so it's not much better. She contributes to the housework 1 day a week and complains about it every time, expecting to not have to clean on her days off since "we're home all the time" and she "already works so hard"

I understand that she is probably cheating on me but I have no way to prove it and even if I could, divorce would only lead to me not seeing my kids everyday. So now I'm stuck between a rock and a hard place: do I just stick it out for the kids since I'm all they've got or do I throw in the towel and risk never seeing them again. She refuses to talk for more than a few minutes about anything uncomfortable preferring the ostrich tactic of ignoring a problem until it goes away or becomes moot. She claims I want to "talk things to death" if I pressure her to continue the conversation or drop it to bring it up later.

I'm not sure really what to do moving forward so, here I am…

(tl;dr) Wife is probably cheating and is abandoning her family and I don't know what to do. (P.S. TN, USA)