How to use Sonos Amp (inside house) powering Sonance 6.1 outdoor system with projector or TV?

I think you can also buy a soundbar like the Beam (Gen2) or Ray and with this connected to the projector in the Sonos app you can set as another room so with enough wifi you can play the "TV Sound" with the soundbar and after selecting the other room (with your Sonance) and all are gonna sound :)

So if I'm following your thinking, once connected to one of these soundbars mentioned above, the Sonos infrastructure will somehow share that signal to the Sonance speakers, even though there isn't an audio source being physically fed through the amp? I guess it makes sense, as in theory it is no different than just streaming music through my phone. Employing that same rationale, would it also make sense that it would work with a Move 2 portable speaker? If so, I'm guessing I would need to add line-in adapter. 

Sonos has the grouping feature that allows you to group 2 ‘rooms’ to play the same audio in both rooms.  For music sources, the music is in perfect sync.  For TV audio sources, the room connected to the TV plays immediately (to sync with video on the TV) while the grouped rooms will be slightly delayed, creating an echo effect.  I don’t think you’ll be happy with this solution, not to mention the soundbar is not built for outdoor use.

The Move 2 isn’t designed to connect to the TV.  You can use a line adapter or use the TV as a bluetooth source but it will be delayed slightly and you may notice that the audio doesn’t match the video on the TV .  That said, you can group the Move 2 with your outdoor amp ‘room’ and it will be in sync, no echo.  I would go with this route over using a soundbar.

The ideal solution is to wire an HDMI cable between the TV and the amp, but short of that, I would use bluetooth.

What would be the source of the video?

While wireless HDMI is becoming available, wireless HDMI-ARC or HDMI-eARC are very uncommon. (And in my opinion not yet ready for wide distribution. That’s why I will not recommend any.) If you are not attempting surround sound outside, there are relatively easy ways to get wireless stereo audio back to the AMP. If you use an analog audio input to the SONOS system, there will be a delay in the audio. On the positive side, I don’t think that the delay will be as annoying in your outdoor setting as it would be in a Livingroom.

You could turn things around, avoiding the analog delay, by placing your source indoors and use the AMP’s HDMI connection, with a splitter and wireless HDMI video transmitter to the Projector. This  is currently available technology. You may need to be creative when remotely controlling the video source.

Thanks to all who replied with suggestions and problem solving. The original goal was to buy a relatively inexpensive protector and screen to watch a movie by/in the pool as a birthday party idea for our daughter. Later, I found out it is a "Mama Mia" theme and they were counting on using the pool speakers, since it is a musical and they want it loud. It is very unlikely that this setup will get much use beyond this birthday party. With all that in mind, and given that there doesn't seem to be a very reasonable solution, I think I'm going to pivot to simply using several Ultimate Ears Bluetooth speakers that can be linked up together. My buddies and I all have them, so I can borrow them and set them up around the pool. Pretty much all of the projectors have Bluetooth functionality, so hopefully the latency isn't too bad.