1) The battery monitor will only show the correct amperage if it is wired correctly. Given the strange other connections you have I would not bank on it, and suggest you check that against the NASA instructions: www.nasamarine.com/wp-content/uploads/2015/12/Clipper-BM1BM2.pdf
2) Why is the domestic battery linked to the ignition circuit? Something very wrong there.
3) In case there's something wrong with the way the battery switches are wired, try disconnecting (i) the engine battery; then (ii) the domestic battery (both with and without the engine battery disconnected), observing any change in the battery monitor reading.
4) Assuming the batteries and battery switches are correctly wired, and you have tried removing all the fuses in the domestic circuit you are aware of with no effect, there must be something else connected. I suggest you (i) try temporarily removing the main positive wire providing power to the switch/fuse panel, just to make sure that there isn't something wrong in its wiring that's rendering your fuse removal ineffective; then (ii) follow the positive wire(s) from the domestic battery to find out what else is connected to it.
Hi Richard, I would try disconnecting the alternator as a quick check, just take off the retaining clip and uplug the connector on the rear of it. It could be that your weird cross connection problem is leaving the field coils with power running through them. John is right, the electrical power for the engine should come only from the engine battery.
Check if any house lights or navigation lights are on by mistake, stuck switch or are directly wired. It's just plain weird there is no ignition key or switch. How does power get to the starter solenoid? Is any equipment or cable anywhere warm to touch? Refrigerator running? Stuck bilge pump? Until you find the fault, suggest disconnecting the batteries at the positive posts when not on boat. GOOD LUCK, and do let us know what you find.