When I'm at home, I use an adapter and plug my TT into a 20 amp outlet. I've heard that you shouldn't run your A/C when only plugged into 20 amps, but the breaker for the A/C in the TT is only a 20 am...
Are you using any kind of extension cord to plug in? If so, make sure it's a beefy cord and not just your everyday orange one that's 50' long!
If you do, you'll lose a lot of volts and it will get hot pretty quick.
If you are connecting directly from the 30a trailer cable to the adapter to the outlet, you should be fine as long as you don't run anything more than a few lights.. No water heater on electric, no fridge on electric, no microwave and no hair dryers for sure!!