Is there a way to train a corgi to not eat out of a certain food bowl?

I recently (just over a month ago) moved in with my boyfriend and his mom until we can get a place together, and of course my little boy came with, they already have 2 small dogs that they buy different food for (small breed and a very cheap brand).

The problem with this is that even after my dog has ate all of his own food, he will still try to sneak and eat there food! This isn't ok for a few reasons, the main one for me is that this different dog food doesn't have the same amount of nutrients as what I give my dog and when he eats a fair amount of theirs it causes him to have diarrhea. And that's something no one wants to clean up, especially out of carpet!

For a few weeks he was good about leaving their food bowl alone after a week+ of me giving a stern No and pushing his mussel away from their bowl when he'd go to eat. But he's started to pick the habbit back up now. Is there any way I can train him that that bowl is completely of limits, or do I just have to keep up telling him no (now I've started to crate him when I hear him crunching on it) until he stops again, or until we get our own place?

I trained him to eat when I feed him (roughly the same times every day), while they put food out and it'll sit there all day until it's gone.

I already asked them about putting their food bowls up but they don't want to do that considering their dogs have learned that when they want a snack, well there it is to eat whenever. So putting their bowl up and out of the way isn't really an option.

And I don't feel this is "because he's still hungry" kind of thing, because he still tries to go for it not long after eating his own food when I know I've given him enough.

Any advice or help?