Since you appear to be in FL, this may not apply, but most of the solutions up here in frosty bureaucratic Canada have looked like ducking under the wing of an already established non-profit, whether it's one that runs a community bike shop, or promotes cycling locally, or something of the like.
I'd assume something like Cycling BC, where you pay yearly dues and what not to enter races and are covered with liability (totally talking out of my ass here, someone who's actually a member/leader will step up shortly no doubt) would be the easiest way.
Best to use the infrastructure others have worked hard to create, if your groups can coexist nicely.
Polo can always run a "skills camp for kids!" during the summer and come out looking like champs.
Excited to hear how you navigate it.
There are a ton of mentions of insurance for tournaments on other threads (http://www.leagueofbikepolo.com/search/node/insurance), mostly for tournament hosting purposes, but i don't think anyone has solved this issue at the club level. Perhaps London England. But the solution might look different in different countries.