If your cabinet is secure and the top is what is moving some when cleaning I would suggest using silicone under the countertop ontop of the cabinet. There are generally corner braces on the cabinet where you can put the silicone thick enough and then let it dry well. After that you can caulk the joint with whatever caulk you like for the look. This is the method I used as a plumber installing bathroom cabinets with non wood tops. Good luck