First of all, I am sure the wiring will NOT support 20 amps. Probably all 14 gauge wiring, and that means 15 amp max. A 1500 watt blow dryer takes about 12.5 amps. That only leave 2.5 amps or 300 watts left. You have stuff running on 110 volts when plugged in, like your converter, that draws 100 watts or more. Guess you better get her a smaller wattage hairdryer. Else she needs to dry her hair when you aren't watching television.
You might could add a breaker and run a dedicated plug somewhere, but that is not always easy. Depends on layout and how many walls you have to run through, etc.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT