1. Your face and looks are not a protected class. You can even be fired because of how you look. If they have a dress code, you do need to follow it.
2. Use your head for a change and tell family members to stay the hell away. They do not belong there, period, ESPECIALLY while you're working.
https://www.eeoc.gov/laws/types/harassment.cfm
Harassment is unwelcome conduct that is based on race, color, religion, sex (including pregnancy), national origin, age (40 or older), disability or genetic information.
You have options. You can grow a thicker skin, you can change your style of dressing - I would start laughing at this nutjob - tell your family to stay away or you can quit.