These are a few thoughts on a subject that has many variations regarding charge needs and the many configurations different equipment may require.
the tow is wired to charge the battery from the tug alternator its charge regulator will adjust to the needed charge in most cases (check equip. specs for vehicle)...if
your wise, you will have in the least a battery isolator in the tug so the tow battery cannot drain the tug...they will charge together and drain separately. Battery isolators need to be matched to the vehicle charge circuit configuration.
Beyond this basic set up there are variations and gadgets aplenty.
If you choose not
to use the battery isolator having the tug and tow share the charge circuit that is o.k. not best....but
unplug the tow every time you stop any length of time.
In the case of the tow using a deep cycle only battery
the advice is not to charge it faster than 10 amp hours...you need a gadget to limit the charge from the tow to that limit.
There are hybrid batteries that are deep cycle/start batteries.
.. they can be charged over the 10 amp deep cycle rating and work around that limit not needing the gadget.
The real reason
to consider wiring so the tow and tug share a common charge circuit is this...when the refrigerator is being powered 12v in transit
...its 12v draw is significant needing a steady replenishment of charge as it operates.
Or in my case I run the long desert distances running the refrigerator
on A/C using my inverter.
90% of the time I use the charge/converter to charge it at home the day before camping and do not worry about it...I run 5 days on battery then run my suburu/robin generator
2 hours and its done for another 5 days.
I prefer to leave the fuse out of the charge circuit thru the tug tow plug unless I really need it.
Others have habits different from mine with good reasons for them, when there are more responses I am sure it will be clearer how you want to do this.
Happy Camping, Safe Trails.