I am not familiar with how your setup is suppose to be wired, I can just share this.
Take for instance a heating/cooling system that runs both. Each system has it's own 24V transformer with C or a common. Most T stats are just a switch, they have no need for 24V to work, just 2 wires (more if cooling from same stat), they work based on temp rise or fall depending on what season your in. They have batteries for a display. That is why there is an RH and RC terminal that are normally combined. You can run 2 transformers by removing the link from RC to RH or the jumper sometimes which is flipped around. The transformers cannot "buck".
If your wifi needs it's own 24V power source then you may need to isolate it and it's outputs I imagine run the stat. Your not low on amperage, all this stuff is low amperage, your back-feeding something.
R or red is hot 24V - for heating RH or cooling RC
C (usually the black wire if not used, sometimes the blue if not a Carrier system as blue is cooling) is common 24V
W or white is for heat.
Y or yellow is for cooling.
G or green is for the fan motor.
Somehow, I'm not sure you have it hooked up right. Regardless of whether you are in cooling (need a fan wire and a wire to run the air handler and condenser) or heating, any additional wire is for common.
Show me some wiring diagrams, show me the type of stat, one boiler only? or also an air handler for cooling on the same stat?
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