Cora was like a lot of unbalanced parents who impose their dreams upon their children, not unlike many football parents or gymnastics parents, etc. These are the sorts of people who say its for the kids but if anything goes against them attacks a referee.

Rumple affected them the way he affects everyone; he finds a way to give them what they want in a way that he gets what he wants. It doesn't matter if what he is giving them is good or bad for them or anyone else. The only possible exception is his relationship with Belle, and even then the dagger switch trick will, I suspect, bite him on his ass as far as her love for him. Rumple's redeeming aspect in that relationship is that he knows he's not good enough for her.

Cora wasn't a particularly good person before she lost her heart, so I don't think getting it back would do much good. But the show is a little vague on the issue of how displaced hearts changes people's personalities.