You have two differnt things.. First Streaming on park wi-fi is not really the best of options. many parks have limted bandwidth and if you start streaming video during prime time you won't be happen and others won't as well.
BUT if you wish to improve park WI-Fi two suggestions depending on your level of expertise;
Wi-Fi Ranger... This is an all in one solution consisting of an indoor module. (Router) outdoor Module (Wi-Fi Adapter...looks like a MODEM to the router) and cable. You stick the outdoor module up high and aim it toward the park's Access Point.
Second is a Home Brew Wi-Fi Ranger.. Ubiquiti Wi-Fi device (mine is a Nanostation Loco M-2 which is at the low end of their impressive products)
And a home router (I do not recommend BELKIN which is what I have) And you set it up yourself Alas it does not always work but it really helps.
The other option is to improve yoru CELLULAR data range.. Now you are using your own bandwidth here so nobody in the park will be upset with you hogging it.
We-Boost or Max Signal... These consist of 3 parts.. Indoor antenna. outdoor antenna. and "magic" box (2 way booster) can give you many times the Cellular Range. I have not used one of these but from what I know. Make sure you get the model (or one of them) that works with your cellular provider. And Direcitonal antennas outperform omni. but omni is easier to set up.
And as with any radio system HEIGHT is MIGHT so run 'em up a flagpole
Finally.. Have you considered DISHnetwork for Sat TV?
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times