As an option...
There is no reason you can't get a 2-zone AV receiver that can run a proper surround setup in zone 1 (the main family room), and can still run any and all sources plugged into the receiver in the main zone as well as a second zone (outside).
You can get a Sonos Port to playback audio to the outside, or stream audio inside. Just make a single connection between it and your AV receiver and it will play audio fine in either location. Plus, if you have other audio than what is playing on the Sonos, that can be used inside or outside as well.
The output of the amplifier would be connected to an external amplifier to run the outdoor speakers. You have to consider how many speakers and the impedance considerations of how they are connected. I am a fan of 8 ohm speakers and a multi-channel amplifier as really good ones can be had for about $400-$500 on eBay.
Outdoor subs add low end to the listening which is nice, but they aren't a requirement. A nice 6.5" or 8" outdoor speaker generally sounds good.
None of these are 'rock concert' speakers, but are good for general listening. Once you are outdoors, you have to add a massive amount of speakers for really loud sound, but for general reasonable music listening, you can get by with patio speakers, rock speakers, in-ground speakers, and a long list of others. The in ground speakers are nice because they typically have a omnidirectional sound to them which fills up 'spaces' in all directions nicely. Rock and patio speakers are very directional models that push the audio in a specific direction. Covered areas, like a porch, can use standard in-ceiling speakers just fine.
I would typically consult with a local AV company and get recommendations from them if this was all brand new to me and I wanted to discuss it with someone in more detail. You certainly aren't limited to a single solution, but I would struggle to get a single 125 watt Sonos and expect that it would nicely handle half a dozen speakers outside to a reasonable audio level.
