50amp work except SAT TV but Gen 2 rescue WHY?

If it's not the inverter, trying turning the circuit breaker on the post off and back on. You may only be getting power on one of the two hot legs. Both sides are supposed to trip if one does, but I have seen instances of that not happening. Another possibility is a problem with the transfer switch with one leg not making contact on the shorepower side when the generator is off, but connecting to the generator when it's running.