Hmmmm... I would contact Ross corporate for the policy on pets. It could be that during the holiday season they are afraid of shoplifters putting goods in the stroller when no one is looking - who knows? But if that is the case, they should have a sign posted. Some places make you leave backpacks when you go in - they could do that with the stroller. Of course they don't make people with children do that.
I was at Dillards on Saturday, and there was a woman with a little dog. No one said anything to her. I would change stores, and boycott Ross.