Hey Jim,
I've got a few questions but first, for terminology sake, with the intellitouch there are 2 boards... there's a main motherboard and a personality board (i5 for you) that plugs into the main motherboard. The relays/transformer/sensors/rs485 etc all connect to the personality board.
The relay breaker is the center breaker and where the transformer connects to the personality board you'll see the center two pins are marked 18VAC... that's the transformer coil that powers the relays. If you have a multimeter, I'd give the transformer a quick check - unplug that 6 pin transformer connector from the personality board and check for 18 volts ac at the two center leads.
As for the low voltage breaker...
1. Do the valves and the intellitouch controller still work? (if the motherboard isn't totally fried I would expect they would still work... electronics are on the 12vac breaker, and the valves are on the 24)
2. When does the relay breaker trip?... right when you turn the system on, or only when any (or a particular) relay is actuated?
3. Does it trip if the transformer is not connected to the personality board (this should be unlikely, but would indicate a transformer problem)
4. Does it still trip if you disconnect all the relay signal wires from the personality board (label them first!)
5. Has any component been recently changed or was the system running fine, then just started tripping?
My guess is something on the main motherboard is messed up so it's drawing too much current to close the relays.