[Gaius]

Illusion, even without a Mars colony, parents (and other legal guardians) already have the the right to force their children to live with them, wherever that happens to be. I doubt Mars would be any different, legally. Sure, it might suck to grow up on Mars as a kid, but there are worse places to grow up on Earth. Any Mars colony would have access to all basic necessities, like Coda said, and probably some amenities as well.

As for the child's citizenship status, I think it works just as it does on Earth. If the child is born in a Mars colony that is considered U.S. territory, or if they are born to American parents during an expedition to Mars, then they are an American citizen at birth and may later run for president.