Thinking about getting a travel trailer or class b and wondering how I can legally carry firearms with me.

I live in SC and have a resident CWP there as well as a Utah non resident. I plan to start out in the southeast where my cwp covers me but may eventually travel farther.

What am I getting in to? Do I have to worry about state or national parks as well as state lines? I may like to have my 270win if I were to do some hunting while camping, maybe an AR, and as a minimum my handgun. I thought about asking on a camping forum but thought this would be a better place.

Thanks