We use a gate hook at the top of the basement door. The hook is just long enough to hold the door open far enough for the cats to squeeze through. We've also done the baby gate thing that Roxy describes, and that works well. I'm not sure that either would work for you because your dogs are so small.

My kitties have disliked every self-cleaning and covered box that we've tried. Good old-fashioned flat pans for them!

What about a cat flap with a magnetic latch? The cat wears a fob on her collar, so only she can "unlock" the flap. The fobless dogs wouldn't be able to get through....