Sharon,
Just as an aside. I am assuming your Garmin is reading the engine battery, and that you are reading the 10.8 V when you get in the boat and turn on your Chartplotter. I say this because if you have the Chartplotter on and start your engine the draw from the starter will reduce voltage considerably until the engine starts and the alternator kicks in a charge. With that said, and assuming that you are looking at voltage when first getting on the boat, your engine battery should be at full charge, not 10.8 V. You should only have to put your parallel switch into on position if the battery is too week to start the engine.
You need to figure out why your battery is so low after sitting a while. How old is the battery? if this is an issue of constant low charge you should do a load test on the battery. If the battery tests good you need to figure out what is drawing it down.
As far as the need to use the parallel switch to charge the batteries, if a battery bank is below a voltage threshold of 9.5 V then the relay will assume something is wrong and will not close to allow a charge. I am going to assume however (and I could be wrong) that you have a direct charge from the engine to the engine battery so once the engine starts you should be able to switch the parallel switch back off. If your house batteries were to fall below 9.5 V and you started the engine then they would not charge unless you turned the parallel switch to on and they charge up higher than 9.5 V. Once above 9.5 V then the relays should kick in and you should be able to turn your parallel switch off.
