In my family, we're pretty straightforward and use the proper terms because they are what they are. Body parts are natural and shouldn't be treated with taboo and awkwardness. Occasionally we do refer to them as "my little girl" or "his little boy" to be funny but generally we stick to the proper terms.
My parents, especially my mother, are very typical conservative Singaporeans so they almost don't even mention it at all cost. For me, I use the term "private parts" so it's easier for me to explain why she's supposed to keep it private and only for herself to see.
I taught my children the proper names of their genital, i.e. vagina and penis. During normal days, we will use nickname to call it instead. In our dialect (foochow), we called female's one 'kipkip' and male's one 'bibijiu'