There are a few ways you could go about fixing your counter top, but none will be easy and will require time to do.
The first and most obvious would be to replace the counter top completely with all new. You might have to hire a contractor to install or if you purchase from a cabinet store, have them install. Or, use your local RV dealership and have their service department put a new counter on. If you are comfortable with it, you can do that yourself too.
The second option would be to strip the vinyl off and replace with new by gluing either vinyl or Formica. I've done Formica in the past, but it works only if the edges of the counter top are squared. Unless you have specialized tools and equipment, it's pretty hard making Formica curve over rounded edges and corners. But on square edges, Formica is easy to work with.
The third option would be to anchor down the affected vinyl, or glue it down again very, very well, then use a counter top re-paint method, or resurfacing.
We did this once in a previous house and it turned out pretty good. I patched up the broken (Formica) and filled the cracks, holes, and chips with filler, then used a paint resurfacing kit.
Here's a link to a web page claiming these are the 5 best products to do this.
There are many YouTube videos show how to resurface with these types of kits also. They are done in steps. You prepare the surface following instructions. Then you apply a base coat. It's like a paint, but much more endurable. Once you have the base coat on, you use a specific color to create your patterns, then a second color, and depending on your kit, may even have a third. Between each application, you have to let everything dry. And then when finished, put a final top coat on to seal everything down.
The one we used about 14 years ago was the Gaini. And it was good then. I'm sure it's been improved even more now. Anyway, the end result is awesome!