Heating and cooling question

Trying to figure out how 24 volt electromagnet relay of thermostat works in a heating and cooling system: Background is: Heat system is outside wood boiler, hot water in, then to an air handler for forced air, controlled by a standard thermostat. Central air unit on the bonnet as well. Honeywell 24 volt furnace relay. Has a simple 4 wire thermostat, works fine.   
Last year I added a Weil Mclain tankless boiler on the hot water lines coming in, thinking it could take over when I'm out of town in the winter. The tankless boiler has it's own 24 volt internal system for a thermostat, so I initially added a separate thermostat on the wall next to the first one to control it. Works but the air handler fan kicks on and off with one thermo, the boiler with the other...hard to sync the two ....I'd really like to run both off one thermostat and just shut the gas boiler off with a switch on that thermostat line when I'm not using it. Seems to me that if I put a second electromagnetic switch on the original air handler system and hook the thermostat wires from the tankless to that-- switching one side of the thermostat wire to the boiler on and off instead of the power to a blower motor- I'd solve my problem.
Will just hooking up the red/white thermostat wires with a jumper to a second relay make it function and keep the two circuits separate?   Looked for a wiring diagram of how they work internally but haven't found one yet.
thanks
     

You can accomplish that with one; two stage thermostat. The second stage heat would operate the tankless heater. Use the existing relays in each system but only the transformer of one, probably the current air handler, just exchange the 49va transformer for a 50 or 75va to handle both loads. You woul have to pull at least a 6-wire thermostat wire to the thermostat; common, R, G, Y, w1 & w2. W2 again would be the tankles system.