Does this particular isolator have a way to adjust the operating voltage? If it does /not/ (e.g. just a dumb solenoid) this you should connect the coil to an ignition hot signal or a switch otherwise the two batteries will always be connected. You might consider double redundancy, an ignition hot source then through a switch so that it doesn't try to parallel the batteries as you turn the key from off to run to start.
If there is some way to set at what point the solenoid works then this will be fine. You'd want to make it active when the alternator is working, so higher than 13.5V or something like that. When the alt stops the batteries shouldn't be higher than like 12.75V. It might be called a voltage sensing relay or similar. Just something that figures out if the engine is running or not before paralleling the batteries.
Seems right otherwise, (alt +) to alternator and starting battery, (+) to secondary household battery, (G) to ground.
'91 Pickup - Imelda / '08 Tacoma TRD - Donna
'09 Kawasaki KLR650
'98 Rhygin Juke SS / '12 Gunnar Rockhound 29 / '16 REEB Dikyelous
"Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty. Nobody is able to achieve this completely, but the striving for such achievement is in itself a part of the liberation and a foundation for inner security. " --Albert Einstein