It's 100% legal to "Conceal" it inside of the vehicle. No license required. Good luck and have a safe visit.
FYI, Corpus has a lot of crime. Always something in the paper everyday about robbery. Everybody that I know gets their vehicle broken into when they go down there.
You can legally carry from your vehicle to your temporary residence without a license as well. So dont leave the gun in you car.
Also, while traveling in Texas, you dont need a license. You are exempt to unlawful carry when traveling. Just remember, when you reach your destination, your travels have ended, so dont carry the gun around town when you get to Corpus, leave it in the car.