I run a small operation in SW Florida and make my own boxes and frames. I used to own and run a cabinet shop here until the bottom fell out. I did a lot of testing on glues and Titebond came out on top every time. Titebond III is their waterproof glue. Any of them will break the wood before they break the glue IF the joint is built properly. IE a tight fit. I use a single 18 ga. nail in an air nailer on each joint just to hold things in place until the glue dries.
Regards
Joe