Hi, I've never redone a camper interior, but re-done loads of formica in the past. The best way I've found for removing the old laminate is to work your way across with an old iron to heat up the glue and a scraper or big old chisel to scrape it off ( a word of warning though leaving the heat in one spot too long will cause the laminate to pop off in patches, firing bits into the air). Be careful not to dig into the plywood as well as it will need filling before you stick the new lainate on, or like buddysbuddy says, it will show through. Make sure you give it a good sand down first before sticking the glue on. Cut your laminate so it hangs over the edges, about 10mm all round ( if rounded corners are needed leave them square for now as they will easily trim off later). Apply Evo-stik contact adhesive to both the ply and the laminate, spreading a nice even layer across the full area you are sticking the laminate to (use a ridged spreader). Sticking the laminate together can be a pain, but another good tip is to lay some thin strips of wood across the panel (on top of the dry/tacky glue) and lay your laminate squarely in position on top of these strips. (Make sure there is nothing laying on the glue before laying the laminate on, as the smallest bit of crap will look like you've left a brick under it by the time its stuck down). Working from one side, remove the strips of wood one at a time, pressing the laminate down onto the ply as you go until you reach the otherside and they're all removed. This should ensure your laminate fits nice and square to the panel with no bubbles underneath. Once its all pressed down and your happy with it, trim the edge off with a laminate trimmer in a router. This can be done with a file but needs a bit of skill and can chip the edges if your not careful.
Hope that made some sense, its really not a hard job you just need to be patient and don't try to rush it.
Cheers..