I've used dozens of rolls of painters' tape, and never had any strong enough to delaminate a true wood veneer. Maybe your best fix would be to just replace the door(s). Your RV supplier will likely have a perfect match, for not much $$$.
And then use some fine wire, tightly wrapped around one or two of the hinge pins, to keep the door from opening. Or just install a magnetic catch , which some RV cabinet doors often have from the factory if not equipped with spring-loaded hinges.