There’s nothing you can do. They’re allowed to set new rules for the common areas. They’re not significantly burdening your ability to have a dog, so appealing to your lease isn’t going to help. If they didn’t allow you to use any entrance, then you could make an argument that they altered the lease terms since you can’t have a dog in your apartment without bringing it through the common areas. The “burden” of using the service entrance isn’t enough.