I agree that the bathrooms are the safest place (or any building that has few if any windows). If you can remember - grab your bike helmets! There's a much higher probability of you getting hit by flying debris (or the hail that often precedes a tornado), than getting sucked up in a tornado.
As far as pets go: they're coming with me. The park can sue me later for breaking their rules.
If you can't make it to a shelter - for God's sake don't stay in your death-trap RV. A ditch is safer than an RV.....