Having had a live in MLCer for 18 months myself, I think you will find that you will be able to get your bearings better with her gone, as long as she doesn't just keep "popping" in. You might want to change locks, just saying. I changed locked about a week after mine finally moved out, was it "legal" no, but he kept stealing joint property, so I was done. He monstered about calling the police and I said "Go Ahead". He didn't and I no longer felt crazy because I'd go to look for the waffle maker and it was gone.... BTW, he never made a waffle in his life.
Sorting everything out is exhausting. Finding the paperwork, getting dates and numbers and everything is so overwhelming. But again, one day at a time. Just keep putting one foot in front of the other and eventually you will wake up one morning, everything that needed to be done will be done and it will start to look better. I am sure of it.
As to the "put our differences aside for the sake of the kids to make this easier for them", that translates to sweep it all under the rug and act like everything she did was just fine so she doesn't feel bad. Now, if you WANT to do that, fine. But if you don't you are not obligated to. You can still be distant relative polite when she is around, "for the kid's sake". I attended my D's college graduation 1 year after the divorce, 3000 miles across the country. XH was there. We stood on either side of her and she got pictures. We went to dinner with a group of people and I was at D's side and XH was halfway down the table. We never had to speak to each other at all. It's is amazing the conversations you can have with a group of people that include an X, and you never have to speak to the X or acknowledge their presence at all. If you didn't know better, it would almost look normal. D thanked me afterwards. She was very happy she could have pictures with both of her parents. Now, if OW had been there, would I have been so accommodating? Depends. And D knows that, and quite frankly at this point respects it (it was a long 9 years to get here). You will get differing advice from differing people here and elsewhere. All I want to say is you do you. Be true to yourself because you are who you have to live with for the rest of your life. But do whatever you do because it is right for you and your kids, not because the MLCer thinks you should. JMO. And as always, your mileage may vary.