Lazy Daze Owners' Group

Your problem could be that the batteries are sulfated and are only accepting a surface charge. This means the batteries look good as far as charged voltage and current acceptance is concerned, but if you checked them with a hydrometer, the readings would be unacceptable.

You'll be much happier with two batteries, I think. But you'll have to find a place to put them that can be vented to the exterior.
Flooded-cell batteries 9such as the 6V Trojan T-105s that Lazy Daze uses or the 6V batteries from Costco that you mentioned) emit hydrogen when charging. So the compartment they're kept in must be vented near the top to allow the lighter-than-air gas to escape safely, instead of building up to a potentially explosive mixture.

If you buy 6V batteries, they'll need to be wired in series to give you 12V. Don't forget to include a circuit breaker in the positive line--code says it should be within a foot of the battery.
 "if it is suppose to be installed under the sink somewhere, how do you run the wires that are in the engine compartment?"
 There's no place in an '83 Lazy Daze where you are "supposed" to put two batteries, because the factory didn't design it with that in mind.
That doesn't mean it's a bad idea! --just that unlike LDs built from 1985 onward, your 1983 coach doesn't have a dedicated outside battery compartment that can hold two batteries. You're going to have to improvise: find a compartment that you can fit your batteries into, make vent holes near the top of its lid, and reroute your wiring to it.

You'll need to run very heavy cable from the new batteries to the converter/fuse panel, wherever that is, and medium-weight cable from the batteries to the isolator (located under the hood). You'll probably also want to remove the existing wiring from the old factory-installed "auxiliary" (coach) battery under the hood.

if you're not familiar with high-current, low-voltage DC wiring safety, get help from somebody who is--or hand over the job to a professional RV tech. This isn't like rewiring a flashlight; the currents involved here can easily start a fire that will burn down your rig in a scant few minutes. If you're not sure of what you're doing, don't risk doing the job yourself.
 If this all sounds like a lot of work, it is. Your reward will be much more freedom to use your lights, fans and so on. As a bonus, since you won't be pushing your batteries as hard, they'll last a lot longer. :-)
 "Does the 1983 LD have a built in inverter to use the 110v outlets? Or do I have to buy a 400w inverter and connect it to the coach battery?"

As far as I know, the factory was not installing inverters in 1983, and they have never provided an inverter that powers all the coach's outlets. If you want AC power, you'll need to buy a 300W-400W inverter and wire it directly to the coach battery or batteries. (Plugging it into a 12V cigarette-lighter jack will only get you about 120W, regardless of the inverter's rating.)
 Keep in mind that heavy use of AC appliances will drain your battery pretty quickly. If you only have one battery and one solar panel to recharge it, an inverter is best used for light-duty jobs like powering a laptop computer, cell phone charger or the like.

Andy Baird http://www.andybaird.com/travels/