C., I do understand your frantic anxiety. I'm guessing you don't know this man very well and want him to see you as more perfect than you are. So, take a few deep breaths, get out paper and pencil and make a plan with the realization that if your father-in-law doesn't accept you as you are it's his loss.
Just pick up and put away (shove it into a closet if you have to) as much as you can. I carry a laundry basket with me as I go round the house. Then I can stash it out of site and I don't have as much walking.
Perhaps you have a friend who would come in to help you.
As to the couch. My daughter just uses soap and water. Put just a dab of soap on a damp cloth and run it over the spot. Then use another damp cloth to wipe up the soap. If you can do this each time there is a spill or close to the time the spot will wash off more easily. I'm guessing that if something is left on for several weeks or months it may not easily wash off.
for no red meat, dairy problem: Use grains and lots of vegetables. I would ask him what he can eat. I have lots of food allergies and I appreciate it when the host/ess asks me. Then your hubby and his father could go shopping for some male bonding time. lol
If he eats chicken or pork ("the new white meat")
meals will be easy. How about eggs? Cereal, toast, and fruit are great for breakfast. He may appreciate cooked cereal.
And while this is happening keep reminding yourself that you're a wonderful person that his son has chosen. Dwell on happy things and don't fret the chaotic house and food. What is important is that he have a good time. Good times happen in a cluttered, even "dirty" house. I know from experience.