I had a safe in my toyhauler and was able to bolt it to the floor because there was a storage compartment underneath. Use a steel plate on the underside and sandwich a second one between floor and safe if you need to distribute base weight. I used carriage bolts with lock nuts on the inside of the safe.
I would not worry too much about left to right weight balance in your TH unless it is a small one with low payload capacity. You could put one smaller safe in each forward corner if balance will be an issue.
BTW: I have seen a rolling mechanic's tool box bolted down after the wheels were removed. Locking cross bars secure the drawers in place and foam cutouts are in each drawer for the weapons.