You can carry in your vehicle unlicensed as long as it's out of sight. Doesn't matter if it's loaded or in reach.
Texas castle doctrine is stand your ground and isn't limited to just your home, but anywhere that you legally allowed to be. Like a hotel room that you are renting.
Pretty sure that all of the laws relevant to your question can be found here: http://www.txdps.state.tx.us/Interne...rms/CHL-16.pdf