As long as your callsign is in the FCC database that is all that matters. There's no legal reason to carry a paper license with you unless you just feel like it. Also keep in mind that channels 15-22 are also repeater outputs and there are a growing number of GMRS repeaters out there so if possible try not to interfere with their operation. Our local group for example uses 16 because 15 is the output for our local GMRS repeater.
If you're trying to stay 100 percent legal the UV-5Rs and UV-82s aren't legal for use on GMRS because they lack FCC Part 95 certification. BTECH does sell a GMRS version of the UV-82 called the GMRSV1, but max power is 2 watts on high and low power is 0.5 watts. It is one of the few certified GMRS handhelds that will do repeater operation and will hook to an external antenna. IIRC WOUXUN also has a certified GMRS handheld that will do repeaters and has a 5 watt output.
As for antennas. If all you are going to run is GMRS and not run HAM as well I would go with a dedicated commercial band antenna instead of a dual band HAM antenna. GMRS is mixed up in the Business band so an antenna tuned for that area 460ish-470ish mhz should perform better than a widerbanded ham antenna. Also don't get too wrapped up in longer/higher gain is better. Different tools for different jobs. Higher gain antennas are typically better for flatter more open terrain and the lower gain antennas are going to be more suited for varied hilly/mountainous terrain where the group will be spread out by height as well as distance.
Antennas take up basically no space so if I was going on this trip I would carry a little 6inch 1/4 wave or 12 inch 1/2 wave antenna (half wave is typically known as no ground plane antennas, I believe some 2x 5/8ths fall into this category as well) for tighter more grown up areas and rougher terrain and a longer 5/8s or 2x 5/8s antenna for the road and more flat open areas.
Here are 2 budget options from TRAM/BROWNING. They won't break the bank but will get the job done well and be reliable.