@camryn22014 Large animals are often more difficult to render than small ones, although it would be strange to be able to play with horses and not dogs. Is this just in one save, or in any, and have you tried with different large dogs?
And, this is just a random guess, but is there a bathtub on the lot? The game will constantly try to calculate routing to the tub to potentially give the dog a bath, even when it's not necessary, to the point where these calculations can supercede other necessary functions. If there is a bathtub on the home lot, try removing it and see whether it helps.