Is it necessary to renew the marriage contract in the event of the wife's return to the marital home, given that the husband did not utter a divorce nor intend it, and he had previously divorced her with a single revocable divorce and taken her back three years prior to this incident?

If it is true that you did not divorce your wife except for the single divorce after which you took her back, then she is still under your marital bond. Her separation or her staying in her family's house does not affect this. It is not permissible for the wife to leave her husband's house without his permission, and if she does so without a valid excuse, she is considered rebellious (nashiz), and her right to maintenance is forfeited. The husband is permitted to discipline her according to Islamic law.