Even if it required a bit of effort to remove the carpet and prep the floor for vinyl, I would go that route. I would not want to leave the carpet in place and cover with vinyl or laminate, as that would trap odours, dirt, mold, moisture, and all forms of creepie crawlies between the two layers.
Dave W - 2013 Escape 19', 2013 Escape 15B and 2011 Toyota FJ Cruiser
"You've got to be very careful if you don't know where you are going, because you might not get there." - Yogi Berra