You've pretty much described United Economy Plus. I'm not sure it's even typically that much of a premium although I'm not sure as I get it as part of my status.
From what I've seen, Economy Plus only offers 5" additional legroom and no additional shoulder room. The legroom comes in handy more for ingress and egress (and, I suppose, not having your laptop screen crushed as readily when the passenger in front of you reclines).
The parent specifically asked for legroom. You're correct that there's no additional shoulder room. As a relatively tall person, the legroom is nice. I basically never use a laptop in flight.