With the kids, I would explain to them that it is *never* okay if someone asks them to keep a secret from Mommy. Never. This is what abusers do -- not that your MIL is an abuser, but teaching children this lesson will be an important defense against abusers, if that should ever be an issue.
As for your MIL, I think you need to decide whether you trust her enough to leave her alone with your kids. If you do, then maybe let her know that yogurt is not okay, lying is not okay, and asking the children to keep a secret is not okay. Maybe get her side of the story, too (not that it makes a difference, but she will feel heard). If you don't trust her anymore, then make other arrangements for childcare.
My experience is that the more people who care for a child, the more this comes up. Everybody wants to feed them sugary things, so that they (the children) will like them (the adults), or animal products, so that they will get all this great nutrition that they are supposedly missing.
It is very frustrating. I can't control what other people do when I'm not around. But I can have a discussion with my daughter afterward about how that food was not very healthy.