I think just removing the wallpaper and and painting (instead of adding more wallpaper) would make a big difference (particularly in the bathroom). Also, I would get rid of the current mirror in the bathroom and replace with a smaller framed type, paint the cabinet and new hardware. Honestly, I think just paint will make a world of difference in your space.

I would suggest you take out the cabinet that is to the right of the stove and use it elsewhere in the house -- perhaps in the bathroom or dining room with a hutch above it. Then, I would suggest you have someone install a lazy susan cabinet in the corner between the sink counter and the stove, meaning you would move the stove down a bit and have a small cabinet/counter top to the right of the stove. I would suggest you have the cabinets refinished in white and then paint the walls a pastel you like. If you would prefer white walls, then add white-painted crown molding and paint the ceiling a light neutral blue, such as Sherwin Williams Niagara Falls Blue. Then, I would suggest you choose a favorite accent color and use this sparingly in accessories like towels, pot holders, small vases or floral arrangements, and a valence above the triple windows. For a genuine 1940s look, you might have white ceramic square tiles with a rectangular red border installed as a back splash behind and above the stove. If you are replacing counter tops, I would suggest a light color such as white with a beige or light grey vein or striation for some sort of pattern. You might be able to find the same color and design in floor tile OR opt for a wood floor as another poster suggested.

Doesn't look worth it from that photo!

If it's brand new, have you tried asking the supplier what they recommend? We got a booklet from our supplier when we got new carpet with ways to treat various stains on that particular carpet. Each kind of carpet will be different. Also, have you tried a professional carpet cleaner? If all else fails, try your luck with your insurance company - I know others who have got carpet replaced because of bad stains - depends on your policy.