1) AC/Heat would require a sizable Inverter. 3KW?

2) Your Engine(s) can only supply about 600W each on their standard
alternator.

3) Do you really want your inverter on the starter batteries?

Your inverter should be setup on the Deep Cycle House Batteries.
Leaving the Engine batteries to start, Nav lights etc. You can get a
charger that will run off the 12V starter batteries when the engine(s)
are running that will charge the deep cycles. But typically you don't
want your deep cycles directly connected to the alternator, as it's
charging profile will damage some deep cycle batteries.

Running even a small airconditioner off of inverter could pull 150 Amps
from your storage batteries. You would need to plan on not exceeding
50% of you battery capacity, so you would need 300Amp-Hr for each hour
of cruising you planned on taking. And your available space for
batteries on a 28 footer will be limited.