Pellet stove setup with fan running all the time

[brack86svo]

I have a breckwell big-e pellet stove. I installed a programmable thermostat and hooked it to the stove. In the on/off setting, the stove will turn on and off according to the demand of the thermostat. I installed some duct work off of the furnace and put pusher fans near the ends of the ducts. I got a transformer and relay to hook to the thermostat so the blower would turn on and off. I hooked one side of the transformer to RH on the thermostat and the other side of the relay. G is hooked to the remaining side of the relay. If i turn the thermostat on, the relay kicks on even when heat is not being commanded. I think it had something to do with the pellet stove feeding a voltage to G, the transformer and stove are just not working together. I found that I have 10vac at the G wire when no heat is commanded and the full 25 when it is. If i unhook the two wires that go to the stove when heat isn't commanded, the fan will shut off like it should.

My question is, how can I isolate the two so they don't interfere * In a DC circuit, I would just use a diode to eliminate the power backfeed but, I don't know how to fix this issue with an AC application. The relay I have can be triggered with either 120 or 24, so worst comes to worse, I could tap into the stove blower wiring and use it as a signal to activate the blowers but, I am trying to not do this if possible since I like the ability to control the fan auto/on from the thermostat.

[MTI STUDENT]

The G terminal on a thermostat is used for the fan in cool mode only , but if you was to use the w terminal it would turn on everytime the thermostat called for heat.