The issue here seems deeper than his sulking really, though that is not a helpful way of dealing with problems! But the sulking is a response to something, a symptom not a cause!
I think that to find a way forward you and he need to have a proper conversation about how each of you feels, really listening properly to each others perspective. From what you have said so far this looks like:
You:
*love helping out when needed
*love spending time with your family
*see the helping as a way of seeing more of your family
*know your daughter relies on you but don't mind
*don't agree with his comments about being taken advantage of , don't mind if you are!
*are fed up of his sulking because you are with your family
He:
*doesn't like the amount of time you spend with /doing things for your family
*thinks you are being taken advantage of
*gets cross/moody/sulks when you are doing things with/for your family
*thinks you are doing your daughter no favours long term as you always "rescue" her
If you look at those lists, can you perhaps see the different views of the same scenario coming through? That is why a proper conversation is needed, really listening to each other. Followed by a discussion about ways forward to deal with the issue together that works for your partnership as well as your individual needs - acceptance of viewpoints, compromises, acceptance that the other might just have a point maybe?
I do also think that you need to think carefully about ensuring your daughter doesn't end up falling flat on her face if and when you can't help so much!