All advice here are suggestions except for one that is an order:

DO NOT MOVE OUT OF THE HOUSE...until your attorney says you can.

You guys are in a rush to sell the house, but as soon as you are out, I can pretty much guarantee that will change. If you move out and she is there, then:

1. She has a massive advantage in determining custody, child schedules, and thus child support and alimony.
2. She can force you to pay child support + any spousal support + half the mortgage and bills.
3. There is nothing you can do to speed the sale of the house.
4. She can effectively hold out for years by refusing showings, or keeping it messy. As the resident, she probably will get to set the asking price too until you can get a judge to issue orders, which will take years of hearings and appraisals that you have to pay for.
5. She can stop paying the mortgage and still live in the house for possibly a couple of years, then declare bankruptcy, and the lender will come after your assets for their loss.
6. She can move her new boyfriend in, and you will not be able to do anything about it, and you will still be paying half of their living expenses.
7. She will never return to the marriage as long as her new relationship is better for her than what you offer - how do you think the balance will look when she has you paying half her living expenses as well as enough for a monthly getaway with her new boyfriend?

Don't think this will happen to you? I have seen this happen dozens of times, and none of those men ever thought that this would happen to them. You move out, and you are asking for these things to happen.