BTW - is your dad on FB? If so, how about just posting a nice photo of the finished work and saying something publicly about how great your dad is for doing this for you. That way he can feel thanked and you don't have to open the door for a private discussion where he tries to get you to pay part of it.
Honestly - do you think your dad just overpromises - like he WANTS to be the generous dad but then finds himself in over his head? Or is he just stingy and starts to rethink it after the reality of what he's spending hits him? Just so you know, either way, this is not normal dad behavior. But it's what you have so just figure out how best to manage him.
Also - re: your daughter: I think this is just typical teen stuff, but just wonder if there's any possibility she's heard or surmised something at her father's house that is affecting her behavior towards you? For instance, I imagine if she had in any way confronted her father or his wife over the fact that their relationship started as an affair (am I right in remembering that she's figured that out?) then it's possible that one of them defended themselves by somehow putting the blame off on you. Might be worth just listening closely.
(My aforementioned son who said he used to think his father "shat gold" was relating to me how my ex, towards the end of our marriage, would complain to our son that I was "lazy" - which I absolutely was not, I was exhausted due to a medical condition. It took time and son having his own medical problems, which his father was not sympathetic about, for son to see the truth about my ex's behavior towards me.)