Hi Elaine,
Welcome to the PC forum!
Regarding flat-towing your Outback. There are two things to look into.
1) Call the general Subaru customer service number and ask to speak with technical support. When you get connected to the right person, ask if you can flat tow your specific model Outback behind a motor home.
2) Search the internet for suppliers of tow bars and related, like Roadmaster and Blue Ox as a couple of examples. If they make the hardware to connect your Outback to a tow bar, then you have a chance. Subaru might tell you it is okay to do, but you surely need the permanently-mounted hardware to mount a tow bar.
Some vehicles, one model with a particular 4-wheel-drive option could be flat towed, while another model might not. Our Jeep Liberty 4x4 has a transfer case, a separate shift lever to select 2-wheel-drive, 4-wheel-drive-high, neutral, and 4-wheel-drive-low. The same Liberty which is not a 4x4 (a 2-wheel-drive without that transfer case) is officially not allowed to be flat-towed. When we tow our Liberty, the transfer case must be in neutral, but the regular gear selector with P-R-N-D-2-1 must be in park to prevent the automatic transmission from moving while being towed.
Well wishes in your research. I seem to recall seeing a couple of Outbacks being flat-towed, so maybe you have a chance.