It sounds like you have a choice of putting up more wallboard with the patterned wallpaper or a faux-tile, putting up drywall, or putting up some other kind of paneling. I know that Swanstone makes a wall board that looks like subway tiles. It would mean that the walls all look tiled, though. Swanstone generally is adhered to existing drywall with construction adhesive so may require that the wallboard you have be in good enough condition and strength to do that. There may be other faux-tile wallboards, too. 30 years ago I bought one that looked like tile that was pretty nice. It was called Baker Board.

You probably need to determine a couple of things before you go shopping. Does your home have standard stud spacing? Are the studs wood, or metal? Are the existing panels adhered well enough to standard studs that you can use it as a base to work off of, or do you need to remove the panels and put up drywall or other wall material first? If you peel off the loose wallpaper covering, can the existing wallboard be used to glue (construction adhesive) onto, or will it crumble or otherwise not be a good substrate to glue to? These questions may need to go to the home manufacturer.

You might find that hiring a GC or consultant who works with mobile homes will work best with this project, since they are used to the construction standards involved with this kind of wallboard. My mom and sister lived in a double-wide and we found quite a few shady companies working in the field in our area, but good ones are out there if you get good references.

Lowes has a nice, inexpensive beadboard panel.

https://www.lowes.com/pd/47-75-in-x-7-98-ft-Beaded-White-Hardboard-Wall-Panel/3031277

Or an inexpensive white wallboard that goes on the wall with construction adhesive. https://www.lowes.com/pd/47-75-in-x-7-98-ft-Smooth-White-Hardboard-Wall-Panel/3015239

Or a fiberglass wall panel that look like tile, but is more expensive than the others. https://www.lowes.com/pd/48-in-x-8-ft-Embossed-Cotton-White-Sandstone-Fiberglass-Reinforced-Plastic-FRP-Wall-Panel/3150231

There are other fiberglass and plastic wall panels of different textures, too. There is also shiplap and wood paneling galore. I got halfway through the 30 pages of Lowe's stuff on a "wall paneling" search. Saw a ton of shower walls in Swanstone, Kohler Choreograph, and Transolid. Ignore the shower wall panels, you do not need this level of waterproofing in a bathroom. Of course, there are a lot of other stores to look at, too (my sister works at Lowes ;-) )

Thank you very much, Nancy. All your suggestions are good ones. In fact, they seem better than the recommendations of my neighbours who have the same issues with aging prefab homes in Florida. They opted to paint on top of wallpaper on top of the original Wall board. To me, that sounds like masking a problem with a temporary solution.....?