What changes would be needed to a late model rover to enable it to function under water? What would prevent a rover from functioning under water as is?
Make it a submarine. Years ago, NASA conceived of a Europa exploration mission into the ice mantle. The "Cryo-bot" or Melt probe was a nuclear powered heat plunger, once it melted it's way thru the ice, it would deposit a swimming probe for underwater exploration. HOwever that's was only verifiable if they could confirm that Europa's under surface was liquid, ice or slush.
Adapting an existing rover design to work underwater would be extremely cost prohibitive and it would be cheaper, more effective, and all around a better idea to design a whole new rover with underwater capability in mind.
In a general sense, there's a couple problems that an underwater rover needs to counter:
Pressure: Most spacecraft and rovers function in a near vacuum environment. On Earth, even at just 10 meters of water depth there is already 1 atm of pressure
Communication: Water is notoriously difficult to communicate through
Power: Sunlight doesn't penetrate water very far even without ice above it. An alternative power source to local solar panels is needed.
Corrosive environment: Salt or other chemicals in the water can cause corrosion or fatigue in all sorts of materials
If you wanted to recycle a rover such as the Curiosity rover to work underwater, basically the only think you'd keep is the RTG. Everything else would need to be replaced and redesigned.