Huh? Your post seems to support your family's perception of you. You admitted that you spoke to your mum a day after Thanksgiving and you had not done the work at that time. Thanksgiving falls on Thursdays. So you weren't there to do the work by Thursday as you promised. You conversed with your mum on Friday and spoke of going on Friday (a day after Thanksgiving).
Either you have your days screwed or you actually are inconsiderate as your mum thinks. Honestly, I don't think you owe them anything. But if you do promise to do something, you should live up to it. If you can't do something, then don't commit yourself. You aren't obliged to, so don't. Stop trying to make up for things by doing such work for them. Your mum needs to learn her priorities. It seems to me that she puts her fiance ahead of her child(ren). If that's what she wants, fine. But then you aren't obligated to commit to do things for her or her fiance, in my view. The whole thing doesn't sound like a repair thing as much as it sounds like a frictional relationship waiting to reach its climax soon. Settle the relationship between all parties, then there'll be better communication, trust, and less tension going on.
Hey, this is my perception of the situation. I have not claimed that it's some divine truth.