The River Oaks Chamber Orchestra in Houston offers on-site babysitting for ages infant through 10 with music and movement activities during its 5 p.m. concerts. The 5- to 10-year-olds "receive humorous instruction in audience etiquette and visit the concert hall for one piece of music." Parents have the option of extending care so they can get dinner out after the concert.
I think there could certainly be demand for something like this in Richmond for symphony matinees. Young musicians in the Richmond Youth Symphony Orchestra could be hired in a work-study arrangement --they'd get their orchestra tuition paid, they'd get experience in music education, the Symphony would get more families into concerts, kids would feel not so much like they were being ditched at home.
The Seattle Symphony offers musical birthday parties -- they've got Soundbridge, kind of like a children's museum dedicated to music. But there's plenty that could be done just with the space and resources at CenterStage. Any parent of a 3- to 10-year-old has likely taken their kids to jumping parties, rock-climbing parties, science parties, skating parties, mouse parties (or is he a rat?), art parties... are there Civil War parties around here? Probably. Anyway, the market's huge. The Richmond Symphony already has an arrangement with a Music Together teacher who teaches group classes... this could be expanded into parties, maybe. Or get music ed majors from VCU.
I'd bet money that the RSO has already discussed these ideas but need the funding/staff power to get them going and market them. By the way, I just saw on their website today that they are having open rehearsals, and free at that, but in sort of a field-trip format for high school and college students by reservation only.