One thing for sure, your battery has seen better days and needs replacing. We all got the crappy batteries from our dealers when purchasing new, first trip out I noticed the new dealer battery having difficulty holding up with demand.
Whether you have an underlying issue or this is expected operation, a dual battery set up will pay dividends by letting you use all the latest technology on your new RV for longer periods, particularly if you choose golfcart batteries.
Use a voltmeter to determine proper function of your electrical system, ensure the converter is indeed applying the proper charging voltage to your battery, hopefully you will notice that it changes as it goes through various charging stages.