File for divorce, sell the house, split the proceeds in an equitable way, and move on.
We get that you don't want to live with her, but get the paperwork done. It's nice that you can make the mortgage payments, but in order to keep the house, you have to buy out her share of the equity in the house. While you're paying those mortgage payments and not filing the paperwork, equity it be a building.
Until someone files for divorce here, it is unambiguously marital property. It was purchased during the marriage, most likely using a down payment that involved some amount of money that was accrued during your marriage. By your own admission, she contributed to the mortgage prior to moving out. So no, it is not solely yours.
Until someone files the paperwork, commenting about child support - or lack thereof - is irrelevant. There is no court order for child support, so it need not be even mentioned. Unless, of course, you have been sending child support for the child still living with your wife.
It is very possible for a father to get the house and the kids in MA - I've had 2 female relatives who had that happened to them in MA, and frankly, the judge's ruling in both those cases made sense. At this point, the fact that you've been making mortgage payments and she has not been living there is in your favor, so get the paperwork done rather than procrastinating.