How old does a child have to be to choose to go to the non custodial parent's house

They are never old enough, they will be old enough to testify in court what they want, but until they are 18 they have to follow the court order.

So if they want to live with the non custodial parent the non custodial parent will have to file in court for custody

To add to what Chuck says, some states do issue guidelines that the courts will go along with the child's wishes as long as they deem its in the child's best interests. But the decision is always the courts, not the child's.

To get the court to make such a decision, one of the parents needs to petition the court to modify the custody agtreement.