Well with due respect to all, as i have rights to express my opinion.
If i were u, i wouldn't have gone there knowing that its a so called "Family Day" without my family, (racism/favourism whatever).
As we say in my language 'Apni izzet apnay haath mein hai' meaning your respect is in your own hands.
If its mentioned that its a family day why challenge their rules, no matter how wrong/racist. You sneaked in earlier as u mentioned maybe you were lucky or they didn't noticed you, it was just not your day.
I personally wouldn't even bother to go there esp. on certain days, they allow certain people so be it, coz if i'm stopped, its me who is humiliated no them.. so to save me from that agony i would rather stay at home..
Again, no offence to anyone, its purely my humble opinion i could be wrong.

Better luck nxt time :)