" Sounds like you need some estimates from local craftsmen that can
inspect your kitchen and see what can be done. I don't think vinly
is any better than any other covering on an uneven surface. In fact,
I consider it the worst. "

While I agree the job should be done right by leveling the old floor if
at all possible and that she may not be happy with the results if she
doesn't, why would sheet vinyl be the worst material? I would think
it would be one of the best as it's flexible and has few if any seams.
What's better then?

Vinyl tiles? Pergo? Wood? Seems all over to open up
Ceramic Tile - Will surely crack
Carpet - Poor choice for a kitchen

What's left then?