I agree with most of the advice here, Clare. I especially like FarNorth's idea about letting DS and DIL know in advance when you're available.
And I totally understand about keeping the hair appointment. My own family knows I won't cancel/postpone my hair appointments unless there's an emergency, LOL! My hair doesn't cancel/postpone getting out of control, and I think I have a right to look nice, unless there are more pressing concerns.
Still, I understand your inner conflict over this. And if you were never there for DS and DIL, I might be saying something different. But you've given them a lot of your time. You have a right to some time to take care of yourself.
I'm sorry if DS and DIL don't understand that. But maybe they're too caught up in their own issues right now to think of anyone else. I'm also sorry that the other family member told you what DS and DIL are feeling. That was out-of-line, IMO, and only served to upset you.
How reliable is this family member? Are you sure you can even trust what they told you?
Regardless, I may be wrong, but I detect a mild criticism here of continuing to breastfeed at GD's age. While I don't think it's the usual choice (my DD breastfed each of her kids for about a year), it's not unheard of. As others have suggested, that has nothing to do, by itself, with GD's waking up at night. She simply may be a light sleeper or she may be having night terrors. Do you know if DS and DIL have spoken to the doctor or the HV about this problem?
Even so, DIL could begin to solve this problem by starting to wean GD. She might still get up at night, but then DS could take turns comforting her. Or, if they don't like that option, DIL could pump some of her milk into bottles, so that DS could handle some of those night feedings. How do you feed her when you're watching her? They could deal with these night feedings the same way if they really feel she needs to be fed and not just comforted. My point is, while it's good that you pitch in where you can, I agree with you that they have it in their power to solve this issue themselves (or with the help of the doctor or HV).
Maybe they didn't accept your offer of help on Tuesday or Wednesday because they were upset about Monday. But perhaps that also means they found another way of dealing, which is a good thing. Please don't beat yourself up about it. IMO, you need to just back away a little bit and give them a few days to cool down (if they're angry) and adjust. Then, give them your schedule for the next week or whatever, as FN suggested, and see how they respond. Good luck!