Christine
I think you may be confusing your self, you have what is known as a 'combi' it is an inverter to give you 240v ac from your domestic 12or24v dc batteries, it also has a charger in the same box that will charge your domestic batteries only when on shoreline or a generator is available.
To charge your domestic batteries you can either use shoreline or generator via the 'combi' (charger) or run the engine and the alternator will do it.
This is not or should not be possible, the inverter may be ON to supply the 240v ac but it will not be charging the batteries the charger does that.
Remember the charger only works when on shoreline or generator.
Without shoreline or generator then the alternator on the propulsion engine does the charging.
If you were using 240v ac whilst cruising the alternator will be supply the 12or24v dc to the inverter and then the 240v ac,
If the load is greater than the alternator can supply then your batteries will not be charged, all the alternator power will be going to the inverter to supply the 240vac.
I do not know the Sterling but if it has an output for domestic and start battery (charging) you could disconnect the charge wire from the start battery and connect to the domestic battery with the existing charge lead. You may wish to get this confirmed by someone that knows the unit.