If the outdoor temps are below about 40F, the heat pump will not be very efficient - but it should work on the generator. It almost sounds like your 2nd compressor is not coming on.
FWIW . . . we only use the heat pump when plugged in to shore power, otherwise we use the furnace. It seems to me that using diesel / gasoline to generate electricity, then using that electricity to generate heat, is less efficient than using propane for direct heat.
Norm & Janet
FMCA; WIT; FCOA; Good Sam; Passport