Is it permissible for a father residing in Makkah to come on an Umrah visa without Ihram, with the intention of resting for a few days, and then entering into Ihram for Umrah from the Miqat of the people of Makkah?

If your father intended to perform 'Umrah and passed by the Miqat, he should have entered into ihram from there. It is not permissible for him to pass the Miqat without being in ihram. He must now return to the Miqat to enter into ihram from it. If he does so, then there is nothing upon him. However, if he enters into ihram from Makkah, then he must offer a sacrifice (dam) to be slaughtered in Makkah and distributed among its poor, because passing the Miqat without ihram while intending to perform a ritual act (nusuk) necessitates a dam. If he returns to the Miqat and enters into ihram from there, then there is nothing upon him.