>My question is what would you guys do in this situation?

Hard no. I don't care how amicable the split.

If I'm in her shoes, if I can't afford the house on my own then I can't afford the house, tough cookies but much better in the long run. I'd sell the truck to help pay for the house before giving it to the ex as a bribe/quid pro quo.

If I'm in your shoes, I want to move on and not be tied financially to someone I'm not married to for the next two decades and not be able to get a house of my own during that time. (It's entirely possible that mortgage rates will never again be as low as your current rate during the life of your loan.)