[JRTJH]

Two quick possibilities come to mind. First, if the water overflowing onto the bathroom floor is clean, clear water, I'd suspect a leaking toilet flush valve.

If the water overflowing is "black tank contents" then I'd suspect that rainwater is getting into the black tank, possibly from a missing vent stack cap on the roof??? But even if it is, it shouldn't be able to flow up into the toilet if the toilet flush ball is sealing properly.

So, it sounds like either you have a defective, leaking foot pedal water valve or you have a combination of several problems: Leaking black tank that overfills when it rains and leaks up, into the toilet through a defective, leaking bowl seal.

A third, unlikely problem is the foam seal where the toilet sits on the tank fitting. It's a "wax ring" in home toilets and a "foam ring" in RV applications. If it's leaking, the water from the black tank could be seeping out around the base of the toilet, but that's not what you say your wife described. ???????