Most hair dryers will draw 1500 watts on high, which means you're pulling close to 12.5 amps on a 15 amp circuit with just the hair dryer alone. Add in the wattage for the fridge and *poof*, there goes your circuit.
When I ran the wiring for my second AC, I installed it on a separate 20 amp plug that goes straight to the 20 amp connection on the power pole. I also installed a 110v receptacle on the same circuit, meaning I'm not drawing power for that one receptacle from the same 30 amp circuit the rest of the trailer is on. So...my wife can run the hair dryer all she wants...or at least until she trips the 20 amp circuit.
You could do the same, as long as you're handy with electricity. If not, you can have an electrician do it. Shouldn't take a lot of time.