Heater will not shut off when it reaches desired temperature
This may not be the answer, but here's what I make of it...

Heat pumps have a maximum temperature they can reach when it's cold outside.  It sounds like for you, this temp might be around 70 degrees.

What my heat pump thermostat will do is call for heat when the temperature drops more than one degree lower than the set temp.  So, if I have it set to 70, the heat pump kicks on at 68.5.  If the temp falls another degree or two (mine is adjustable), it realized that the heat pump can't do it on its own, so it calls for aux heat.  It normally won't turn off until the temp is above the set temp, so it would run until the house got to 71 (again, this is adjustable).

What may be happening is that your aux heat is turning on when your thermostat falls to 68, but then it turns off when it reaches 70, but the heat pump stays on trying to get the house up to 71.  That never happens - the temp actually falls back to 68 and the aux heat comes on and the process repeats.

If your thermostat has adjustable points at where aux heat comes on and when it shuts off after reaching the desired temp, you could adjust those so it does turn off.  The other option is to just switch to "Emergency heat" when its very cold outside. The heat pump won't operate and all heat will come from Aux heat.  This isn't normally what you want to do, but in extremes, it could be needed.  Right now my house in Texas is on Emerg heat because it was 15 degrees last night.