let her drop the boys off at your home, she doesn't have to come in, she can bring them to the door and you let them in and then tell her "thank you".
Who came up with the custody arrangement? Is this something she drummed up or is this something you agreed to? Does it work for your schedule? Can you handle more time with the kids? Can you take the kids for an equal amount of time? If so, you should do it and tell her that you've decided you want the kids for half of the time. Come up with a schedule that works for both of you, ie. 1 week + 1 weekend and then swap the kids, 7 days each.
As far as the joint back account, she wants to move out, let her face the reality of that decision which probably involves, working, getting a full-time job, and putting on her "big girl panties" and taking on adult responsibility. She can't just assume you will bank roll her new living arrangements, bills, child support while she lives a life having affairs and seeking out new relationships. That would be dumb on her part and it wouldn't be smart for you to enable her. The real world costs money, let her take care of it, she's an adult, she can handle it, if she complains that it's tough, the real world is tough, nobody is given a free ride, we all have to work to make our way in this world.
