Is it better for my ten-year-old son, who will be performing 'Umrah, to enter into a state of Ihram with us from Abyar Ali and remain in that state until the following day, or to exit Ihram upon arrival and then re-enter it later from Al-Taneem, or to postpone entering into Ihram altogether until after arrival and then enter into it from Al-Taneem?

If you wish for your discerning son to perform Umrah (definition), he must enter into the state of ihram (definition) from the miqat (definition). If you pass the miqat with him while he is not in ihram, and he then assumes ihram from a point beyond it, a compensatory sacrifice (dam) becomes incumbent upon you, as you were the one who passed the miqat with him without instructing him to enter ihram. The son remains in his state of ihram until he is able to perform the Umrah.