I need help. I have a gas Amana furnace that I have hooked to one thermostat (4 wires) and then a second thermostat (2 wires) hooked for only the fan to come on with use of my outdoor wood furnace. When the 2 wire thermostat call for the fan to come on, the outside compressor will come on. It seems the power will “bleed” to the Yellow wire. It doesn’t do this if I just run the fan on the furnace without the 2nd thermostat. I have turn off the compressor, but don't think it good to run it like that.

Wiring on HVAC Control Board to Thermostats
R = Red 24 VAC
W = Heating
Y = Cooling
G = Fan

2nd Thermostat hooked up to the Red for power and Green for the fan.
Compressor is attached to Y & C terminals on HVAC Board.

I have read and been told I need a relay to keep the Green and Yellow apart. What relay would I need and how to fix this problem. Thanks so much for your help.