Thanks for all the wonderful advice! I am definitely going to try the gate to see if that helps. The thing is that they have a doggy door which gives them access to the garden and they run in and out all day, tracking in dirt. I clean them after our walks, but I can't be here to wipe their feet every time they use the garden.
I usually don't really care about these things because dogs will be dogs and I want my dogs to be happy. But the couches I'm getting are a gift from my dad and they've been in the family for years, so I really want to take good care of them. And I'm finally settling in my own apartment and my perfectionist streak wants everything to be nice and perfect

I know it's not possible with dogs, but I just want to find something that works for us.
I'm going to buy some extra fleece fabric to cover the bed to keep it clean. I'll do the same thing for the couches if the dogs keep getting on.
This might be a strange question, but do your Yorkies "respect" your furniture? Do they jump around on it, wrestle on it, etc. I grew up without dogs in the house, so I have no frame of reference.