Paying someone to reupholster your furniture costs too much if your furniture isn't expensive to start with. I have reupholstered furniture before myself. You take off the old fabric, take it apart with a seam ripper (make sure to label each piece where it goes) then use it as a pattern for the new fabric. Sew it together exactly the same as the old fabric, use a staple gun to attach it where it was stapled before.
Get rid of the cats, they will ruin your furniture over and over again.
I hate cats. 
You got that right!! I called a local shop to inquire about a having a couple barrel chairs done (they go in the motor home but are nothing special). The quote? $300 per, plus exra if they needed to have padding or springs!! Not going to happen. I can find new for that.
Cats? Been there. Beautiful oak sectional set with recliners destroyed by warring cats. I cried when it went away in the trash. It had been gorgeous and again, the cost of re upholstering was beyond the cost of buying new, albeit not reclining.
On the other hand I never had mice when I had cats.