Goodman GMS90703BXA Heater "heat pump cold weather problems" Questions

heat pump installed almost 3 years ago and no one has been able to fix it. In the summer, the a/c works perfectly. When the weather turns cold (this week in South Carolina), the heater will work until

...heat pump continues running and I can hear the air handler switching trying to turn on every few minutes or so. I put my hand on the motor and it is definitely hot. If I shut off the circuit breaker ...