Yes, Henry.
Jamaica is the king of resort courses ~ and hence why shallow reefs are destroyed there. Tell your wife to get certified for once and stop being part of the problem
Seriously though, she can do the study at home thing where she does the classroom 100% at home, takes all but the final at home, and travels with her tests. Your resort will accept the tests, do her in-water check out dives (she will be in the water anyway, right?), and at the end take the final at the resort. Zero resort time wasted assuming your DM will let you have a Mai Tia during the exam
Going one morning by yourself won't alleviate your depth problem unless you book that one day on a private charter. Also, if you can't show your resort that you are capable of diving 100 feet and that you've done it regularly before, they will likely not let you go down that deep. For all the pot smoking they do there and their "no worries mon" attitude, this is one area they don't relax on.
But don't get hung up on diving only. You will enjoy it. Its 82 degrees with 100 feet of visibility. Its not Illinois rock quarry boring. And for the record, I have been to Cozumel, Utila, Roatan, Bonaire, and Florida Keys each one time. I went to Jamaica twice - it's a fun place if you know how to have fun. Relax and get your groove on!