Squarepants...A combined Caye Caulker/Cozumel trip is certainly possible and Peter has laid out your transportation options quite well. Another possibility would be a rental car from Playa Del Carmen into Belize City but that would end up being far more expensive than the bus option and the rental car would be sitting in Belize City (not necessarily safely either) while you dove in Caye Caulker. As he said you would be eating up a day, each way, in extra travel time over and above the travel time from Sea-Tac south. While it would be an adventure, I would simply resign myself to treating these destinations as two separate holidays and pick one (flip a coin as they are both excellent choices).
If you go with Belize I think an excellent way to approach this holiday would be to split your time between Caye Caulker and Ambergris Caye to get the flavor of each island and town as they are quite different. Fly into Belize City, change planes and fly into either of the two Cayes and then, when ready to do the other Caye, take a water taxi. The water taxi is the least expensive option between Cayes but, unless you have a group larger than two people, is not a big savings from Belize International since you need to take a $25.00 taxi to the water taxi terminal. It also adds quite a bit more travel time which can be better spent under water or under an palapa with a cold Belikin. When done your second Caye then fly back to Belize International. Peter is an excellent choice as a dive op for Ambergris Caye. As small as Belize is in terms of population, it is still too large to do much more than this on one holiday....unless you are going for an extended period of time. There is also outstanding diving on the southern and central atolls but I personally feel that these are best done from a live aboard.
For Mexico consider splitting a holiday between Cozumel and the Playa areas. This would be an opportunity to do world class drift dives in Coz and then some great reef and cenote diving in the Playa area. There a great dive operators in Cozumel and while the one I use is Living Underwater there are several others who get great reviews on this board. For the Playa area I dive with Diablo Divers/Aquanauts but, again, there are others who receive high praise on ScubaBoard.
If you do decide to do a combined Belize/Cozumel trip then take Peter's advice and go to the ambergriscaye.com message board that he has given you the link for and search the threads. I have seen some very detailed "how to" instructions on the best ways to get from the Mayan Riviera into Belize. It will be an adventure but it is possible. Either way you will be treated to some great diving and nice places to visit. You can do so on a budget if you start looking at accommodation options this far out as there are some good, clean and inexpensive places to stay in each location.