Is it permissible to bring one's wife and son to live in America, given that the questioner travels to them whenever the opportunity arises?

Residing in non-Muslim countries is not permissible except in specific cases with conditions mentioned in Fatwa no. 2007. If these conditions are met, then there is no objection to bringing one's wife and children to reside there, with the caveat that it is not permissible for a woman to travel without a mahram, as explained in Fatwa no. 32835.