I'm not certain, but I think ANYONE the kid lives with can file for support. It might depend upon the state, but I'd think if... well, like it was a single father, got deployed so let the kid stay with an aunt or uncle, the aunt or uncle could apply for child support to be sent by the father while he was on active duty & without the kid... though generally it is already resolved when they get thier orders... they go through a whole legal process of preparing for deployment that probably involves making certain the kids have a place to live & support arranged.
I've also heard of friends of the family getting support if the faily decides to move in the kid's senior year & leaves the kid to live with friends so he could finish out high school & graduate with his same class... stuff like that. I've not heard of it in a divorce situation with step-families... but i'd assume it's the same.
And being that it's the father's wife who is doing the filing, heck, since I assume she's living with Dad & the kid is living with them, the cour twill probably just take it as if he was the one who signed the papers to file even if she's not allowed to file just becuse the kid is living in her house...
But why should it be a problem? Parents always owe support if the kid is not living with them. We get SO upset if a man doesn't wnat to pay... why is anyone thinking that the woman shouldn't pay when the kid lives with someone else?