I'm sorry to say it, but I have to agree with the posters who suggest that perhaps your heart just really isn't in wanting to help with this. You had an impulse of generosity, which you later regretted. I'm not saying there's anything bad about that -- we've all been there, and it does sound like it would be a big job. I don't, though, think your "heart led you astray" -- there is nothing wrong with being kind and helpful -- maybe it just led you to a nobler place than you are prepared to go at this time and for this person.
But where is all this stuff coming from:
... Hazel assumes that I’ll do it whenever it’s convenient for her and the kids.
I’m tired of having this hanging over my head ... It feels like I have to leave room in my schedule every week, although I told Hazel that I would need advance notice. To her, that probably means two days.
I am now dreading the trip, which I expect to be a disaster for me. I fully expect it to turn into a full day of me running them around to pick up things, or getting drug into long family drama conversations that delay the drive back to our city.
Why do you expect "disaster" and "drama" and a fully day of errands? Why do you think she expects you to be at her beck and call? I mean, maybe Hazel has said things that make the you think this. But this is also the kind of narrative that spins through our brains when we feel a little guilty or selfish: we want to get out of doing what we offered to do, because it is a lot of work or inconvenient, but we don't want to think of ourselves as less generous and kind as we felt when we made the offer (or, as vernoaz puts it, as if we were just making empty offers to make ourselves feel good about ourselves), so we start projecting onto the other person to sort of make it their fault that we want out.
I know whereof I speak! I offered our home to some acquaintances for their wedding reception for 50-75 people ages ago, and now they are planning the wedding, and the reception will indeed be at our house. I have to resist feeling slightly annoyed or put upon when they ask questions or for advice, even though they are being absolutely lovely and totally undemanding. So if I ever feel like it's too much, that's on me for offering more than I really wanted to do, not that they are doing anything wrong. And the truth is, I really am glad to do it.
This reminds me of a string some time ago about someone who offered to host someone coming to her city, and then, once she realized she didn't want to do it, was irritated by every little thing her friend said and did. Offering favors and hospitality isn't for everyone. It is hard work and inconvenient. If you don't want to do it, that's fine. But either way, you have to be gracious about it -- either decline politely, or do it wholeheartedly. Don't turn on the other person. (Of course I am not talking about people who abuse the situation. But I don't hear where Hazel has done that here.)
I agree with the posters who say just to let this ride until it comes up, if it even ever does. And if and when it does, don't let Hazel have it, a la "Well, I can't keep my life on hold for you! What made you think the offer was good forever?" etc., as if she were at fault for simply believing you. Just say something like, "Oh, Hazel, I'm really sorry -- I had a lot more time back in the summer, but my schedule has gotten much busier. So I'm afraid you won't be able to count on me now. I hope you won't have too much trouble making other arrangements" or use one of the other polite formulas others here have given. Don't try to get her to agree how reasonable and faultless you are being and how huge an imposition it would have been.
The point: no, you don't have to keep offers open forever, and you don't have to drive if you don't want to. But if you do decline, then do it graciously. Just say no politely and express regret for any inconvenience the failure to button down the timing has caused her.
