Buying a new drill and some screws (I'm assuming you don't have the drill already with you on the trip) would be cheaper than the RV repair place anyway, most likely. So if you didn't mind taking some of your vacation time to tinker with it, you should be able to drill the old screws which will promptly push into the space between the skins when the drill starts to bite, then put in new screws and travel on.
Another assumption I'm making is that you can get a drill onto the broken screws without removing the rest of the screws that hold up this cabinet and temporarily removing the cabinet to get at those broken-off screws, which might be more involved.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill