My Wagan 400W Elite came with clips to connect directly to the battery. It ran fine up to 100W using a car plug but screamed over that due to the wiring, not the inverter itself. Chances are the wire at your plug is entirely too small to pull enough amps. Any inverter you buy will have the same problem.
In our tt, we had two outlets: one that came off of a radio wire (long distance and small) and one that came directly off the converter (short distance and large). We could barely pull 100W off the radio wire without an alarm but had no problem with 200W off the converter wire. YMMV