Have you talked to your kids? They are a bit young, yet, but mine were very understanding about the possibility of moving, and very supportive. I was lucky in that I was able to stay in the house, and happy that I was able to provide some stability and security for them, but they both said that I didn't have to, and they would understand.
One thing I was able to do was refi with the same loan (term and amount), in a package that eliminated all of the closing costs. It just basically restarted the same loan seven years later. I'll have to pay her half the equity out of other assets.
One thing, though, is to be careful about which assets you give her in the D. If you give her all cash and equities, and are credited the same amount in your retirement account, when you cash out your retirement, you will be taxed at around 30%, whereas your W will only be taxed at the long term cap gains rate of around 10%, so you will have given her almost 20% more after tax money than you received.
M:23 T:26 Me:53, Wife: 60 S:18 D:16 filed 7/16 W moved out 4/28/17