Being a women here in Karachi , I can totally relate to you. I myself have also seen girls with hair on face and hands .And I can even feel , that they feel to embarrassed about it.
Even when I was in high school .I had a lot of hair on my forehands .My school uniform was designed in a way that it shows my hand, forearms and arms. I wasn't mature enough to think to get rid of it .But When I see my friends with flawless arms I definitely felt embarrassed and even my friends used to call my hands "jungle ". So it really made me insecure . But as I am growing up I see that my family allows me to take care of myself and they allow me going to salon on weekly basis . Maybe they didnt allowed me back then because they didn't really wanted me to get into facials and all this stuff at a very young age and that is understandable too. Now They trust me and that is what make me feel proud.
I love your daughter hair style.
Honestly speaking as a mom , I would allow my girlies to do anything they want form getting nails done ,to facials and hair treatment but again within limit . All of this if God wills !