My MIL learned very very early that she is not to give ANY food to DS unless it has been cleared by us first. She didn't get to watch him alone until he was 4 because we couldn't trust her, and wanted him to be able to have the words to say no to certain things, and also tell us if she'd fed him anything bad. She tries to get ME to eat meat, and I'm an adult for gosh sakes...no problems imagining her trying to get him to eat nonsense.
As for gum...there are only a couple brands that are safe for DS.
The sugar brands use corn syrup, for the most part, to get the chewy consistency. That's right out for DS, and I think a lot of kids/adults have reactions to it, they just don't know they are.
The sugarfree gums...we don't even use those. Who wants those nasty chemicals? I don't, and I certainly don't want them in my son's little body.
We did give him gum on our last flight home, when he had become ill and lost his EarPlanes and was FREAKING out. He was so scared of ear pain (and so tired) that he actually threw up. The ladies behind us offered him gum, and I took it, because it would help him, soothe him, AND help with the smell.

But that's a one-time occasion (and we'll get the safe gum for future trips), not a regular, every time he sees his grandma, thing.
Oh, and DS is coming up on 6, definitely not just a baby at 2.