Why is thermostat calling for cool when set to heat
My first thought is that the the wires are hooked up incorrectly.
Pop the cover on the thermostat and look at the labeling where the wire to the furnace attaches.
Do the same at the furnace end.
This may make it clear.
Second step:  Check the installation manuals for the furnace and the thermostat.  If you have 12v control for the heat pump, and the furnace wants a 24v signal...
Third:  It may be that the thermostat cannot properly control two devices.  In this case install a second thermostat at a point that is both reasonably central, and easy to run wire to the furnace.