We had a travel trailer for a few years. Tremendous fun and great way to vacation. And we could bring our dogs with us.
Another idea: Install a hitch on the front of your truck and put a bike rack there. Check etrailer.com to see if one is available for your truck. I put a front hitch on my F250 so that I could back my boat into our garage. It was pretty easy to install.
A front hitch bike rack would be very easy to load. The main downside is that the bikes are fully exposed to the wind, so they're going to get dirtier, maybe a paint chip. But it seems like you'll have to compromise something in your situation.