If you look at this site you will see a second regulator and the adapter needed to hook it up.
Depending on the manufactures recomended pressure you can set the second regulator as needed. Just make sure the full flow rate of the regulator is enough for the generator.
If you did freeze your regulator it most likely was because of the Total Draw, generator, refigerator, stove, heater, hot water heater, or some combination of these, that caused the freeze. I doubt if the generator alone would have any effect