Saw your plea for help on FB and came over to read. And - oh - the memories this all brought back. Gosh - you'd think his name was "Chuck" or something.
First off - divorce is a business transaction and as much as it is tempting to go off on him during this time - it doesn't help you or your situation. (I was told this repeatedly and still reacted the way you did.). He will not "get it". He is just about the money now.
Compare to this. Our house was built for our disabled son. That didn't stop him from wanting me to sell it so he could get his bucks out. To heck with the fact I had to move into a house with stairs with an adult son who could not climb them - not his problem!
Neither of you can say whether the kids will use it or not. I think you should decide which is of more value to you - the tub or the AC repair. If it were me - I'd take the tub. I'd figure out the AC with someone else, anyone else but him. I'd never let him in the house again. That is what I did and things got better since I made that rule.
As far as schedules etc - I think some of this negotiating needs to be handled by the attorneys since it is back to being a hurling match between the 2 of you. Divorce can be quite nasty and you and I had some of the worst situations to deal with.
He can't really sell the tub without your approval. If you want it, don't sign. But be prepared - you'll lose something else. Think carefully about what you want the most and what you're willing to concede. Choose wisely.