If the DC fuses are okay, check the ground connections in the A-frame area next to the battery. There will be one or two lugs. These can be poorly installed or corroded. Check the connections at the two mini circuit breakers beside the battery. These also can be poorly installed or corroded. I was upgrading all the wiring there recently in our TT and the positive wire at the circuit breaker literally fell right out of the ring terminal. Actually, I would check all this anyway even if you weren't having problems at the moment. There will be a #10 bare ground wire from the converter to frame on the side of an I-beam. Same there, it could be poorly installed or corroded.
Since there is a separate 20 amp power inlet that gets plugged into a 20 amp receptacle at home or pedestal, both AC units should be able to run fine at the same time (if voltage is good). Does the second start okay?
If you did connect the battery with reversed polarity, you may hear a mini circuit breaker clicking on & off next to the battery (every 10-20 seconds or so) and maybe a rotten egg smell. Friends of ours did that and had the smell and clicking but did not blow any fuses.
If a TT is 30 amps and you have a 30-50 adapter and if you have a choice at a CG, it can be a good idea to plug into a 50 amp pedestal even if you don't need 50 amps. An area or row of 50 amp pedestals will be interconnected with heavier wiring that will reduce voltage drop. Also, 50 amp receptacles are typically in better shape and you have a lower risk of a loose or bad connection. Wiring to/between pedestals in a CG are not sized for a 30 and 20 amp receptacle simultaneously so the voltage drop can be higher. If voltage gets too low, it can damage AC units.
I would recommend getting a plug-in voltage monitor that you can leave plugged in inside so you can keep an eye on voltage. If you have a voltmeter, you can use it to check the voltage at a pedestal before backing into a site. Buying an EMS unit like Progressive Industries make is an excellent investment.