Slow down and think this through. I can't come up with any scenario where it makes sense to buy a new house with this woman at this time, even if she's not on the deed and even if you can afford it on your own. Not being on the deed doesn't necessarily mean she can't claim half of the equity value on her way out the door. And could you still afford it if she took half of everything else that you own (think half the furniture, half your cash savings, (possibly) half your retirement, and on and on; what if you have to pay child support and alimony for some number of years? Would the house be a good one for you if you are in it all by yourself at least half the time, or would it be a lonely place until your D14 came for her visitation?
Lots of good thoughts here ^^^^
Since it's a marital asset, she will be entitled to half, whether she's on the deed or not.
All that being said, if you will be able to afford it (AFTER ALIMONY AND CHILD SUPPORT), and you want it for YOU, then go for it.
M:23 T:26 Me:53, Wife: 60 S:18 D:16 filed 7/16 W moved out 4/28/17