I don't know anything about the configuration of your system, except for the latch and multiplexer. But in my opinion, if the power-supply is steady enough and everything on the controllerboard has been decoupled the way it should be, there is no harm in just tying all grounds together. Many applications I made work just this way.
I have relay and solid-state outputs on many boards and all grounds are usually common to all circuits.
But a way to disconnect power from one board to another is to use opto-couplers in between the controller board and the relay board.
If you still have problems tell us more about what multiplexer and latch you use and how they are connected.
Did you tie the unused SET and RESET pins (if present) of the flip/flop to their appropriate power? If you left them floating this is a good reason for instability. Just a wild guess.