What type of screws for interior walls

I would never attempt to screw anything to a caravan/MH main wall. You need to be aware of where the wiring runs and you could easily puncture something significant, even the outer skin of the body. Instead, I would try to fix the rack to a dividing bulkhead at 90° to an outer wall.

You'd be better off using some kind of "No Nails" and glue it to the wall

Or even drink from the bottle    !!

I agree with above, it is to dangerous to fix to the wall panels as the unknown lies within. If you could fix the wine glass holders to a board or strip of suitable timber then you may be able to no/liquid nails this to the side wall as the surface area is greater. Be warned not to use the water based version as it does not like plasticised or cold surfaces and can fail.

But do you really need wine glass holders?

Colin

Many thanks for all the replies. I'm going to try and workout a better place on a bulk head or similar. If not, take ABM's advice . And Colin, yes, there are some things that are important in life !! 

I have to confess I will only drink wine out of a glass, so I'm with you on that choice. I've found that the Duralex tumblers meet our needs and are more difficult to knock over in the unlikely event you drink a little more than you should have. They are easy to pack a way and the larger matching design are great for a beer.

Colin