I didn't want you to do that
Whatever "that" is, it's done. That's why you are saying did instead of do. This is an expression of regret.
I wouldn't want you to do that
Whatever "that" is, it's not done yet. This is trying to tell someone not to do something.
This can have a "conditional" meaning, and that means there's an if X or because X somewhere that applies to this, either mentioned previously or assumed by the listener.
This can also be a polite or "softer" version of "I don't want you to do that."
This can also be "will in the past" - and basically be a "past tense" form of "I will not want you to do that" referring to something already done - this could be used if a person A did something, thinking someone else B wanted him/her to do it, but A did not want that to be done.