james wrote:

Should I
a) use a 12V to 110VAC inverter and a 110V battery charger connected
directly to one of the house boat batteries - this seems inefficent.
b) connect the battery in parallel with one of the house boat
batteries - is this too much of a load?

I'd say "b", but with the addition of a suitable DC light bulb in series
with one lead of the wiring to act as a current limiter. Connecting a
discharged battery to a fresh one could cause excess current and even an
explosion. A 50 watt bulb, like a car headlight bulb, will limit the
current to about 4 amps and, best of all, will go out when the charge
equalizes enough that current drops to a safe level and it is no longer
needed. Then you can safely keep your trolling battery in parallel with
your house battery, ready to go fishing.