even if her daughter does wear a one piece, her pubes will still he hanging out the sides!
My mother was one of those that didn't let me shave for a long time because it makes the hair grow back thicker, and she did not believe in waxing, epilating or laser treatment!
I started growing breasts when I was 6, i ran down the stairs and said to mum "look look they are getting bigger!" by the time i was 11 I was already wearing a bra and was a B cup. I got my period when I was 10.
Through primary school kids teased me because of my hairy legs, in high school i finally started doing it but mum was angry at me, by the time i was 14 mum had bought me an epilator!
I think it is great that you are bonding with your daughter like this.
If she doesn't want all of her hair removed she can just get the sides waxed and just trim down the hairs.
What works for me instead of shaving use a special electric rasor made by Braun, (this rasor thing is designed that it cannot cut your skin as it does not touch it) it is like a pencil stick, i first wash my self and then sit on the toilet as i find it much easier to manuever to get the hairs all gone! Plus there is no mess to clean up
When ever i shave "down there" i usually cut my self if im in the shower!
So what I am saying is good on you!