Not sure I follow. 100W of solar is a basically a trickle charger to keep your batts charged in storage. beyond that, you want to plug your shore power cord into your inverter to run things? If your inverter is wired correctly it uses your batteries to run your 120V appliances. And one battery isn't going to give you many AHs. Why wouldn't you just plug your shore power into an actual pedestal/outlet? Maybe I don't understand what it is you are asking.
I don't have a place to plug it in at the moment that's why I'm using the panels but my 12v battery doesn't last very long at all without having to be charged and that's only running my small fan at night and my 22" tv maybe 5hrs a day. I have my RVs 2nd battery that's supposed to run the inside but it's not working right now.
