Ralph,
I have four little dogs and one is 11 with arthritis.....so my thoughts based on that...
I have a mix of marble and hard wood floors. I don't have any laminate because it just doesn't perform like real wood does. In face I have Cam Xe (I think that's how it's spelled) and spent less for it than most laminates but its still one of the top ten hardest woods they make floors out of. I looked around and found it at a wholesale place. So if money is a concern and you want good stuff, start looking and surely you will find something that will stand up to Fido, the stuff I have actually sparked when we were running the tiny finishing nails in and hasn't ever scratched. I really like it, and I laid it down myself.
If you are worried about transitions, don't. Just make sure you buy good transition strips.
Also....if you want to go less permanent you can buy the stuff that a lot of hotels have. The ballroom floors most of us compete on are actually pieced together and lift up in 24X24 inch squares that run on top of carpets. I would think if the hotels can buy it...it has to be available somewhere.
As far as my dogs are concerned they like to be able to lay down on the cool of the floor and they have temperpedic pillows, etc. If you are really worried get an oriental carpet and roll it up when you are dancing and then unroll for the dog to walk on.
There are tons of solutions....just look outside the box :~}
Belle