My very slim DS could have done that at three (he's now 5). One time he ate 6 muffins which he'd help make as an educational sort of activity at my friends' house. He'd already had lunch. He wouldn't do it daily. But if he's hungry, he can really put it away.
We are quite relaxed and he's never been made to eat up what he's not hungry for. I think you'd have to try really hard to get a three year old to overeat. I bet your DC will naturally adjust, OP, so I wouldn't worry about occasionally stuffing his face.
Not sure why you are particularly concerned that he eats yoghurt instead of extra fish fingers. Unless it's plain yoghurt, it's likely way less nutritionally sound than fish fingers anyway (thickeners/ sugar). Even if it is plain - really what is the deal with eating it instead of fish fingers? Fish fingers are good protein and it's good not to always expect another course but instead fill up with what you are hungry for - especially if that thing is healthy.
The thing is with the ILs, it's best to let them get on with it. You'll probably appreciate the fact your DC gets a glimpse of other possibilities when they are a bit older. My Mil is so laid back she's horizontal - one time we came back and the bathroom had been painted, the kids had paint literally head to foot (they'd taken their clothes off to paint themselves), it was crazy. No way would they have got away with it if we were in but they had an absolute ball and it actually wasn't so hard to clear up.
You can lose your shit about stuff like this or you can be grateful that the kids get to appreciate a range of approaches and ways of doing stuff. It's way easier on you if you can just let her get on with it. Unless she is going to be doing regular childcare, what harm can it really do? One huge meal at granny's a week does not make for a fat kid.