You can't use the inverter too much. But, you might be able to use your batteries too much. And you can overwork your alternator. So, your question is a little bit of a challenge to answer. And, I can only write about the only coach I know and will assume some of it applies to yours. Of course, opinions will always vary!
My inverter has a setup controller. Of its many functions it allows you to tell the inverter when to consider the batteries "dead". At that point either the generator can be set to start or the inverter will quit making 120. The idea with this is that it will prevent any accidental, excessive and damaging discharge to the batteries. I've programmed mine to assume that a 50% discharge is to be treated as "dead" and the genset will start. So, my first suggestion is that you figure out how to set your inverter to quit when you want it to so that you will get long battery life.
Next, consider how you are going to recharge the batteries. My Beaver is amazing in that it can automatically recharge the batteries from any of three sources and it does it automatically. Best is shore power, second best is the Onan and worst is having the engine alternator do it. I think it should be considered a design flaw that allows the small engine alternator to automatically and routinely run at full output for long periods of time!
So, my second suggestion is to never let the engine alternator recharge the house batteries more than just a little bit. That's because it is tiny compared to the Onan or shore power. It does work its heart out trying and get very hot doing it. Getting hot won't be noticed since you are in the other end of the coach driving, but hot means early failure. Then you will notice it because our alternators are a little unique, sometimes hard to find, expensive and not easy to change.
Another way to put it is that the engine alternator is designed to replace a few amps briefly used from the engine batteries to start the engine and then supply the various needs of driving, like headlights, etc. It is very good at that, but if you ask it to additionally charge four or six half dead deep cycle house batteries you are asking too much!
I think the best practice is to dry camp and use the inverter all you want until the batteries drop to about 50%. Then recharge them with the Onan until the batteries are back to about 95%. If you are about to drive and the house batteries have been used even a little bit, I think you should start the Onan before starting the engine. Leave the Onan running until you think the house batteries are fairly well charged. On my coach, the Aladdin monitor will tell me when to shut of the genset.
Related to this is that the more you use your Onan the longer it will last. It needs to run to keep the windings dry, the parts lubricated and the brushes polished. Using it to charge batteries through the inverter is a good opportunity to “exercise” it.
