I would agree as others have suggested and split up the trip. My wife and I have been doing that lately and will again in January. The outer atolls have the better diving, but not as much for your wife to do while you're diving. If your pockets are a little deeper, Turneffe Island Resort is a pretty good option with a pool, stand-up paddle boards, etc. which your wife can enjoy while you dive. They also usually have a separate snorkel boat and go out a couple of times/day.
If you'd like to base your land options further south you could stay/dive with OFF The Wall which leaves out of Dangriga and stay out on Glovers for a week. Then when you return to the mainland on Saturday you can explore from there or head down to Placencia. Not as much to do on Glovers for your wife, but you can swim/snorkel right from shore there, and they have paddle boards and kayaks, etc. They will also arrange boat snorkels if you like, but everything is so close there. The owners, Jim and Kendra, are great people and I'm sure you'd enjoy it.
We're again staying on an outer Atoll to dive for a week and then rent a vehicle at the airport for a stay south of Belmopan. We've discovered the Sleeping Giant Lodge and the place is just great! It's also pretty central so you can go any direction from there. Lots of things to do and numerous Myan ruins within easy driving distance. With a vehicle you have the option of booking a resort tour and/or explore yourselves. Driving and exploring is easy and really pretty safe in Belize.
One tour that I can't recommend enough is the ATM cave tour. You have to arrange the tour with a company and space is a little limited. My wife and I thought it was one of the best "paid tours" we've ever been on.