Each vehicle is different, and each wiring option brings its own pros and cons. I don't have a Liberty. It shouldn't take long for a Liberty owner or two to post.
Let's take the 12V power first. If your ignition switch (or, if you have to install a battery cutoff switch) prevents you from getting 12V from the toad's battery, you can run a properly-sized and properly-fused 12V line directly from the battery to a location near the Patriot.
If you want the Liberty battery to maintain its charge, then you can run a "toad charge" connection between the coach and the toad. Again, it should be properly-sized and properly-fused.
On which wiring kit works best, it's a matter of opinion. Manufacturers make custom "plug and play" kits for popular toads, and I chose one for our Honda Fit. I see at least two
offered for the Liberty. Because you have that choice, I'd recommend against the "universal" diode kits, leaving the custom kits, the "add-a-bulb" kits, or portable lights for your options. Again, that's an opinion.
If you elect not to use portable lights or to install separate bulbs in the Liberty rear lamp housings, you can have a situation where the coach signals and the toad brake signals conflict. A brake relay can take care of this. On this page from etrailer
, they describe what circumstances will require a brake relay, in the section "Is a Relay Required?"
This is just a brief outline, but it should help you advance your research.