Rather than parroting the ever popular"go big or go home"philosophy,I'll give you suggestions that help you to make calls which fit your situation. Check to see what annual registeration cost's for 12&14k trailers. See what type annual inspection and insurance is required for various weight classes. The difference in above and below 10k Lbs is huge in Texas but states vary. If you are stopped for burnt out tail light,expired registeration or other minor traffic violations and have a clean driving record,below 10k usually results in a warning whereas above 10k is a different ball game. Cost of legally operating a large trailer in Texas exceeds what it cost's for 3 or 4 light duty.
As for keeping battery charged. If you follow the suggestion of jerry-rigging a system that eliminate's trailer battery and alow's using truck battery,you might be s-o-r-r-y. If trailer seperate's from hitch there will be no break-away brakes and things rarly end well. Even if there is never an event where brake-away brakes come into play,you risk a stiff fine and possible high risk insurance requirements if a trooper find's the cobbled up wireing.
This is about the point where drugstore cowboys and short haulers accuse me of Chicken Little behavior. Ask any long time cross country truck driver how they would be treated for disabling automaticly applied trailer brakes. Point(s) being even if your state isn't strict on commercial vehicles,the adjoining states might be if you have occasion to use their roads.
I'm not discouraging you buying a dump trailer,just advise going in with eyes open and/or possibly going with a sensiable size and spending savings on other toys.
For mulch and other light weight material,
look at this