Because ever since downloading it I've noticed annoying stutters. Will uninstalling it corrupt my save if I've bought no houses, used any new items the dlc introduced, or adopted children?

Shouldn't be a problem, you might have a bit of a dirty save, but nothing that'll obliterate it.

Have you tried disabling the .esp first, to see if that is indeed the issue of the stuttering?

If you play skyrim in your PC i think this is what you must do:

Just turn off the Hearthfires.ESM in your Data Files when you first launch the game.

If you want it totally gone, just pull the Hearthfires.ESM and the same name BSA out of the Skyrim Data Folder, then its not in the game at all.

But if you do a verify at anytime Steam will just put it back.