Dear Jamaica Tenant:
I understand your frustration, but this penalty will not support a right to end the lease and move out.
You did express your dissatisfaction to management and they did refund $100.
Taking the landlord to Small Claims Court is an available remedy, but if the court takes the landlord's position that you were fined for continuing the moving in process after 5PM, then you may also become liable for the landlord's attorney fees.
You could try for a better compromise, and suing is your right. But there is risk if you lose.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.