If it were me and my setup is similar to yours, I would talk to the neighbor and talk to the CG and see if it was ok just to charge your batteries to plug into a neighboring post. Having a 2 year old justifies this and if you give them a few bucks (if they even ask for it) , everyone is happy. it's not like it's summer and you are running AC all day. I would love to see someone attempt to charge me for theft for what might equate to a few dollars at the most. Give me a break. I am sure it's not the first time this happened and since you can't run a gen, you really have no other choice to charge your batteries.
Moving forward if you encounter this scenario a lot, I would invest in a solar charger.
But I feel certain you can work this out so everyone is happy. Communication and common sense will prevail here.