Have no idea how they build those units, but laminate is normally glued onto a substrate like MDF. Then the MDF is typically screwed into from below. I doubt the substrate would be glued down. Just look from underneath to see if there's screws. The laminate/substrate counter top will come out together as an assembly.
There should be caulking all around the countertop perimeter which will need to be cut to break the seal, then completely removed before installing new caulking. (If it's silicone, silicone will not adhere to cured silicone.)
When it comes to RVs, not much is straight, plumb, level or square as it should be. You should carefully check before cutting a new counter top. A template may help. If there is a wall at left and right hand sides of the top, you do NOT want to cut wrong or too short... The back wall may not be straight either - so check with a straightedge.
Remove any drawers. It will probably help to remove cabinet doors (by undoing screws in hinges). If a range in there too, you should pull that out - but do NOT forget to reconnect the propane properly.
Are you getting a new top pre-cut to size or buying an over-sized piece and trimming it?