One thing I find curious is the lack of cycling clubs for children in the USA. British Cycling's (BC) Go-Ride programme has led to the formation of 338 Go-Ride clubs nationally (yup, I know we're a smaller, much more densely populated country) and 85% of our Olympic riders have come from them. They vary from clubs with purpose-built facilities to those making use of schools, like the one you refer to, to parks and any suitable other patch of land.
The one thing they all have in common is a national system. BC's national coaching system ensures that standards are pretty much the same across the board and it's supported by annual national conferences (held regionally) on coaching, child protection, volunteer roles, fund-raising, etc.
There's a programme of national and regional youth races in all disciplines with a development pathway for talented riders, right up to potential Olympic competitors. (Youth racing goes from U8s to U16s, tho' there a limits put on the younger age groups, to avoid too many long journeys for them)
I appreciate that the sheer size of the US militates against such a set-up, but surely something along these lines could be done on a more regional/state level. By the way, I started our 52 weeks/year Kids Saturday Bike Club before the Go-Ride set-up came into existence, so it's possible to do it without such support. Good luck to your 11 year old.