I feel for you. Our relatives (one set of grands, aunts and uncles, and only cousin to our daughter) are also very distant (overseas) so we see them once a year and it's also our big family vacation time as well as family visiting time. It's a tough balance.
I disagree with posters that you were being presumptuous all these years to do the planning you did. I think what happened with this sudden rash of "I've planned a BBQ etc." is that one person did it, told the other relatives, and everyone suddenly loved the idea.
If you still want to go to this resort and not cancel, well, as someone said, the various BBQs are only a few nights out of a longer stay. It's too bad, though, because kids this age don't perform on command, and there's every chance that your child will be cranky, or turn shy, or refuse the food they've made, or run off into the house rather than be cooed over by strangers. That's the risk these adults take in showing her off like that. Unfortunately you'll be the one stressed by it as you say "Oh, I'm so sorry, she's not usually like that...." But they are courting it with their plans.
If you go, where you have to put your foot down firmly is on the overnights with grandma and grandpa. Our daughter still hasn't spent a night without one of us there and she's 10; she's just not comfortable with that yet, though she's an outgoing child. Why expect a 4-year-old to be ready? If she visited their home often and was very familiar with it, felt comfortable there, etc. that would be different. But grandma cannot just announce she is taking your child for FOUR TO SIX NIGHTS. One night, if you were close by in case of meltdown, would be OK, but you don't start a young kid on overnights with a four-day marathon and mom and dad hours away.
Grandma is clueless about what will happen the first night when your daughter wants mom NOW and wants to leave NOW and you and your husband are a couple of hours away.
I would just smile and gently tell her, "Sally hasn't spent a night away from us yet, and starting now, on a vacation where everything's new, just isnt' the right time to start. We'll be hours away if she wakes you up and says she wants to see us. It's so nice of you to want to give us this time off, and we appreciate it, but we'd really love for all of us to spend time with you." Don't fuss or fight over it, just smile and drop it and if she persists on the overnights or says "You're coddling her, you have to let her start sometime etc." just don't rise to that bait -- stay calm and say, yes, we will, but she's four. Most kids don't do sleepovers that young unless it's close to mom and dad and in a place they're very familiar with. Then switch the subject to some terrific outing you'd like them to join you for.
It may be that grandma sincerely sees it as her doing you a huge, huge favor and providing you and your husband with a big treat, for her to take your daughter for that long: She sees it as "I'm giving them a wonderful extended break! Can't they appreciate that? Aren't they grateful?" I think it would be wise, and kind, to acknowledge that and say, I know you meant well and it's such a generous offer; I'm sorry to say no; I know you meant to give us a treat and a break, etc. Let her know you understand that she really was excited about her idea. She may feel really deflated that what she thought was a terrific idea you'd just leap at was met with "No." I agree with the no, totally, but at least acknowledge with her the good intentions and be ready with lots of other things she can do with your daughter.
One last thing if you do go -- once you are there, the family members may likely come up with "Oh I thought I'd come to the resort today" or "I want you to come over here today." Be ready for that -- sudden interruptions of your plans. See if you can invite them along on some of the outings for your daughter but do stick to your plans to have some family time with just you, husband and child.