Maybe they're one of those weird families who eat at strange times, like lunch at 4pm? Thought they'd postpone it an hour for you. And then found they were too hungry to wait. DH's parents are a bit like that, or used to be. Don't understand the concept of communal eating. Quite often we used to arrive for Sunday lunch and DH's dad had eaten his and was sitting watching telly in the front room. MIL would get ours out of the oven where it was keeping warm. Sometimes she'd already eaten too, ,but sometimes she had it with us. I mean, I was always grateful for someone else cooking for us, but I always found the canteen atmosphere a bit odd. If you invite family to eat a meal with you, you EAT A MEAL WITH THEM, don't you? 
We never have an issue in my family when planning stuff so there is never any misunderstandings. It's really not complicated.
Mum: "would you like to come for a meal on Easter weekend/whenever?"
Me: "ooh yes, that would be nice, thanks, when were you thinking of? I'm working on Easter Sunday until 5 so if you wanted to do it then it would have to be an evening meal, we could probably get there just after 6? Of if you want to make it at a lunchtime we could come on Easter Monday whenever you like, just let us know what time to get there."
I just don't get how these "everyone's annoyed at each other cos this happened" situations arise when you communicate and discuss plans properly.