How rude

I took my kid to a doc appointment and lowered the blanket on the stroller. This lady says to me “ is this your child because she is very light” before I could say anything she says “ at least you will not have to worry about your little one dealing with racism” I was pissed but kept my cool because my kid is 3 and I didn’t want her hearing my get all upset. She then said “ well is it your baby or are you the nanny” I gave my kid my headphone and I told her off I couldn’t keep my cool any longer I try so hard to ignore it and just mind my business. The office manger then asked the lady to leave and that her and her children was no longer welcome at the office. I just don’t understand how people can say things like that especially in front of a child. Then my kid says to me when we was in examine room “ mom is there something wrong with my color we can tell the doc ” my heart just dropped we had a conversation and she understands that because im black and dad is mixed she is lighter. My baby is light and I’m brown but she is my child my baby my only child she is beautiful,smart and I tell her this ever day and she loves herself loves to look in mirror and play dress up I really hope this does not effect her.