Home audio/entertainment system off deep cycles?

Keep your expectations for quality very low. A decent subwoofer runs 600W with 2Kw peaks, and that's just the sub. A good 7-channel amp is 100W/channel continuous to be able to reproduce clear notes. If you don't expect much, you'll be pleased with the outcome.

http://www.partsexpress.com

Somewhere in there are midrange horns for like four dollars. They sound great and they do not need any type of crossover network.

Choose the highest wattage LEPAI receiver amplifier they offer. It has all the connection points.

For Bass, I would go with a ten inch powered under-seat woofer. But understand, woofers needs LOTS OF AMPS or they sound piffy like laptop speakers. Plan-on one group 31 AGM battery within a 5 foot distance and six AWG charging leads. I is not hard to set up a dedicated charging system.

With such a system as I have described, the sound level would be of immense potential. Spot-weld cracking bass and mid-range guitar and keyboard volume realism that could slam both eardrums together in the middle.

The surprise comes when his system is compared to incredibly complicated and expensive auto sound systems and blasts the competition clear out of the auditorium. Like with many electronics, the idiots that think they know what they're doing reproducing music on speakers haven't a clue. I spent years developing incredibly high amperage Nippondenso, Hitachi, and Mistubishi alternators, for "Northwest Regulator" and the thousands of dollars those kids wasted on car stereos produced sound quality worthy of a 1957 Wurlitzer jukebox. It was pathetic.

I modified many home speaker systems with those Parts Express Magnavox Astro Sonic horns. My favorite was coupling the horns to Acoustic Research AR 4, speakers. Klipshorn Folded Corner Horn speakers were good, as were Altec Lansing Voice of The Theater speakers. But all are gigantic enclosures. What I wrote above is quite small.

I think you're basically on the right track. It sounds like it could be a very fun project, though undoubtedly a good bit of work.

The entertainment systems are generally not going to be consuming their maximum rated power; this is particularly true for the receiver's audio amplifier, assuming it's not a very high end class A amplifier.

I would suggest a pure sine wave inverter for this use, not so much out of concern for the safety of the equipment as for the liklihood of picking up spurrious noise from many MSW inverters that put out a lot of electrical noise. A 1000W unit would be plenty; a 500W or 600W one would probably be sufficient; however, in my opinion the difference in price is small enough that the larger size seems more sensible.

Guessing at a system average power usage of about 200W, a pair of golf cart batteries would last about five hours before getting down to 50 percent charge. Lead acid batteries don't take well to being deeply discharged, and especially to being left in a discharged state; I wouldn't suggest going too much below 50 percent. Lighting, if any, and any fridges etc. would of course add to the power consumption.

For connecting to the vehicle electrical system, you do need an isolator of some sort, which you've basically described. Having a continuous duty contactor (or heavy-duty relay, which is basically the same thing under a different name) to connect the battery banks together when the engine running is pretty straightforward and can be done reliably. Often this is controlled by a switched circuit on the vehicle side, so it's engaged when the key is in the run position. Occasionally there are somewhat more sophisticated schemes, maybe with voltage sensing or time delays or such.

You would be very well served to have heavier wiring between the batteries than a 10 gauge wire. My class C motorhome has, as best as I can make out, 2 gauge wiring, fused at 175A at either end. Charge currents for golf cart batteries can easily be over 50A, and having a thin wire (with its resistance and voltage drop) will unnecessarily slow down charging from the vehicle electrical system.

It would not be a bad idea to also have some sort of an AC powered charger ("converter" in RV parlance). Depending on your usage, it could be a fairly small smart charger, mainly to maintain the battery's state of charge, or it could be a somewhat more powerful one that can recharge it in a reasonably short length of time. Progressive Dynamics makes some excellent ones for the latter use.

I do hope you've researched registration and driver's licensing laws for your proposed uses. In general this would not be able to be registered as an RV, and you'd probably need to have a class B CDL, quite possibly with a passenger endorsement (if it seats more than 15 including the driver), to legally drive it. An RV for personal use does not have these requirements, but does have certain minimal equipment requirements that may vary a little from state to state but typically include having at least some subset of permanently installed sanitation systems (a toilet), cooking systems, a permanent electrical system, sleeping bunks, etc.