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.
So I thought if I took my shore power cord and put it directly into my inverter hooked up to the battery and solar panels that it would work the same way it does plugging it into a regular outlet power source.
I used to do it just like this, it works fine...but it is critical that you disable the onboard converter when doing so. Otherwise the converter gets energized by the 120V AC from the inverter and it tries to do its job of providing 12V DC charging. This will cause it to try and charge the 12V DC batteries while also drawing power from the batteries via the inverter. An energy draining loop is created...
On my TT, the converter AC input was pigtailed into the AC breaker (GEN). I bought another AC breaker from the hardware store, popped it into an available slot in the AC board, and removed the converter power input from the GEN pigtail and wired it to the new breaker. Then I used that breaker as an on/off switch for the converter. You'll have to investigate how your converter is powered and find a way to disconnect it.
Also note that your whole camper 120V AC system will think shore power is available, so don't use things that are beyond your inverter/battery capacity or it will overload the inverter. Make sure a propane fridge is on gas only, water heater on gas, don't use the air conditioner or microwave or other high-draw AC items.
