It sounds like you've already been combative with them rather than asking for forgiveness and a warning instead of the $150 fine. If that's the case, they probably won't budge on the fine. If you want to get a lawyer involved, that will cost way more than $150 and they might tell you you're in the wrong and there's nothing they can do. To avoid future fines, follow the rule. They probably implemented it because other tenants have a fear of dogs, and it's not a huge burden to tell dog owners to use a different door. This isn't equivalent to Jim Crow laws. They want everyone to feel safe leaving and returning home.