That's very very weird. The pedals shouldn't be drawing much power - all that's inside the pedal unit is some potentiometers (or at least that's the case for my G27). Perhaps there's a short circuit in there. That doesn't seem totally plausible though, cos then the potentiometers (or wherever the short is) would be getting pretty hot. If you have a power meter you could see if the (wall-plug) power demand for the PSU is a lot higher when the pedals are plugged in. If so that would suggest the PSU probably isn't the root cause of your problems.
The FFB motor which spins the wheel at startup will be drawing massively more power than the pots ever should.