a source of information about hauling livestock across state lines, etc. is the PRCA the pro rodeo cowboy association. I know there are campgrounds with small corrals, etc all over the country, but can't tell you where they are.
I know there are restrictions on hauling hay...has to be weed free certified, etc.
The rodeo horses also have to have health cards showing vet exams and/or shots if needed, etc.
So start with the PRCA.
as for the two giant dogs.... yes, you'll run into a few rv parks with restrictions based on size, so you'll just have to ask each one. State and Federal campgrounds usually don't ban dogs of any kind, but will require them to be leashed.