Tom stays home. He's got the medical training. He's also got the 50s nostalgia thing, so I can see him being a stickler for insisting in having one parent at home in his nuclear family. Since his wife would grind his teeth into powder if he suggested she quit, he'd gladly stay at home.
Just turn the Paris/Torres quarters into a mini-holodeck and he'll play Captain Proton and Mr. Mom at the same time.
And don't forget the tv. The kid can grow up with a genuine historical brain draining experience.
Shatnertage! Has the new movie wooed you back to the BBS?