Corian is a Dupont product and very durable and repairable as a counter surface. The issue is the nature of an RV. It moves, Shakes, Shifts. Corian doesn't take to movement, either do other countertop materials. The places yours is broken are the places it's trying to move. If I was replacing a countertop, I'd want to make sure the base is solidly anchored. I'd also think about mounting the Corian on a plywood base to absorb the movement.
I started out by saying Corian is repairable. A good shop can epoxy cracks in the countertop that will become as strong as the original and invisible. Burns and other marks can often be buffed out of the surface. Before tossing the old, you might have a shop give you an estimate for repairs.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI