Any day you learn something is a good day. And especially early on in your camping life there will be lots of lessons to be learned. So good on you for beginning the journey. May your camping trips form the best memories ever.
The usual battery dealers install on trailers is an 80 AH "Marine deep cycle" battery that usually costs somewhere south of $100. Such a battery can be recharged from its 50% discharge state by a 100 watt panel in full sunlight (unshaded) but a 50 watt panel won't do so. Certainly a single 50 watt panel won't do more than top off a pair of hardly discharged batteries, and not even that in the shade. Which is not to say that solar isn't a good idea, just that that panel is undersized for the batteries you have.
Conservation of water and electricity are both good lessons to learn and practice. We get so used to having as much of both as we can possibly use, we get lazy and end up wasting a lot of both. I had a friend who spent a year living in a small TT while her house was being built. Because she had to haul water in a jerry can about 1/4 mile, she got really stingy with its use, and got her daily needs down to 3 gallons per day. That was cooking, dishes, bathing, everything. So in theory, when you manage to get the entire family down to 12 gallons a day, you will have squeezed every drop until it screams.
