I understand you want to be with your kids. I miss mine to, but for my situation, It's best that I'm not living at home with her.
It's been almost a year and a half and my boys are adjusting pretty well. The good thing is that I have them anytime I want with little to no advanced notice. Ironically, our quality of time together is much improved over when I actually lived at home. I was consumed with my relationship problems when I lived at home and didn't focus on my S7 & S14 as much as I should. You'll find that a cheating W can be very amicable in respects to the kids because they feel guilty for the breakup of the family not to mention their selfishness when it comes to their own time. This can work for your advantage in regards to the kids. There are acceptations, but I believe that to be the case with my waw. I know my S7 dogs her relentlessly about daddy not living at home and I can tell this gets to her.
If you can handle it, I say no problem, but if it starts to cause to much friction between you and the W, it will only hurt the kids to witness it. Just be careful to recognize what's said in your interaction with your W, the kids pick up on it and they are smarter than we give them credit for.
"It is curious that physical courage should be so common in the world and moral courage so rare." -Mark Twain