My stepmum has this issue as my brothers are 9 & 11 - she wont let them use the mens changerooms alone, they are not allowed in the womens change rooms and majority of the time there is a wait for the family room.

If we go swimming with them we normally cram myself, my stepmum, my 2 girls and my 2 brothers into the family room - there is no issue with nudity but my lil brothers don't like seeing me naked so they turn around while i get changed and we minimise the time naked.
At our local the girls and i are generally the only people using the disabled / family room as it's easier and mroe space for me to deal with 2 girls and i can stand around naked while i get them sorted and THEN get dressed.. i wouldn't mind kids say 6 or under being in while my girls get dressed but curiosity starts kicking in about then and my girls don't like being stared at.