Just to make sure nobody actually tries this ...
When you run your battery cables from the engine bay into the tub to the second battery (regardless of how you isolate the two), never, never, ever try to defeat the isolation to engage that second battery to crank the motor over.
The current draw during the starting process is very high, will generally overheat and melt the usual 6mm cables within a couple of seconds and that may mean your vehicle will catch on fire.
I agree with Krafty about the earthing. For my money, I'd have fuses on both ends of the cable, as close to the battery as possible, because it isn't the other end I'm worried about, it's the in-between bits of the cable being damaged through chafing or debris.
Also, a reminder about capacity: your alternator is designed to only charge your starter battery to about 70-75% of its rated capacity, to prevent it from gassing. Your secondary battery - being fed the same voltage - will be limited to the same 70-75% capacity. Since you should only ever (at worst case) let your battery fall to 50% of its charge to prevent damage to the cells, your usable capacity is just 20-25% of the battery's rated capacity.
By using an inverter in the tub, use a charger like the
C-Tek Charger Series (I have the XS-7000 installed in my caravan, powered by an inverter supplied with power from the vehicle). Your battery will be maintained at 100% of its charge, giving you 50% of its capacity instead.
And no, I don't resell C-Tek chargers or have shares in the company!