@Helphelpx There is an overload of criticising parents and children these days and it creates a lot of societal pressure on parents. I get why you are concerned about your dd touching her private parts in public, even though it is perfectly normal behaviour for that age.
Unfortunately, I do think the societal expectations on parents to be almost perfect can interfere with how we choose to parent our children. And we can become anxious which can affect the way we respond to our children.
Here is a couple of paragraphs from an article that you might find helpful for the issue you came on here to ask about. (And no, I am not going to join in the ranks of picking on you for the terminology you choose to use and I am not going to dictate that you should use vulva instead of vagina either). I taught my daughter vagina and it was helpful when she could tell me that her vagina hurt. And no it was not her vulva that was hurting, the pain was in her vagina. The doctor gave me some useful information about Vulvovaginitis.
And for those being pedantic about using vulva instead of vagina, have you forgotten labia majora (outside lips of the vagina)? For the sake of simplicity, I don’t think it’s wrong to use one word for the vaginal area. (And from this medical fact sheet I have from the doctor about Vulvovaginitis it does refer to vaginal area).
The title of the article refers to teaching proper names for body parts, however the paragraphs I copied and pasted are about how normal it is for young children to touch themselves and suggested way to respond.
https://amp.abc.net.au/article/11708774
Children will touch their own genitals — it's self-soothing, like thumb-sucking. It's not something they should be ashamed of."
She says it's normal developmental behaviour for under-fives to touch and expose themselves (even in public), so just react calmly and positively when this happens.
"What you should not say is anything like 'That's dirty'," Ms Hamilton says.
Ms Hamilton suggests saying something like this if your child touches or exposes their private parts in public:
"It's OK to touch your private body parts but, remember, private parts are just for you. We don't do that in front of other people."