Thank you for your email. You are not being a prude.
Your 6-year-old daughter is becoming more aware of her body and requesting more privacy,which you as a woman and mom have noticed and along with your maternal instincts know that it is important to respect her needs. Girls as they grow older can become very self conscious and sensitive about their changing bodies and need understanding and privacy.
Men tend to feel more comfortable being naked around each other as well as are used to urinating together; so they do need guidance with regards to understanding the privacy needs of a young girl. This includes not walking into the bathroom when she is bathing. Allowing her to close the bedroom door when changing, and always knocking before entering. Avoid changing her clothes in public, especially at a swimming pool or beach.
While safety in public places should always be your first priority and your daughters should never be left unsupervised, I do not think it is appropriate for either of your daughters and especially your 6- year-old ;to be in the men's changing room at the gym. They could wait in the designated child care area at the gym while dad is showering and changing. There should be a toilet for the children in the children's care area where they can change to swim. When visiting the malls I would continue urging their father to use family toilets or baby changing areas which usually have a toilet attached,;as well as allowing your 6-year-old to use the ladies toilets.He should continue waiting outside the door for her and could also ask a mom entering the toilet to keep an eye on her
In a few years her breasts will begin to bud and she may begin her menstrual cycle.It will be important to have talked to both her and her dad about her changing body as well as how to help her adjust to the changes. You may want to consider getting the following books and any other age appropriate books: Me and my body: where did I come from? Claire Lleweylln, My body is private, Linda Walvoord Gerard,The girl's body book, Kelly Dunham.