Yeah, I agree with Cicero. I am all for /teaching/ children that they don't get to demand other people's stuff, especially not a gift someone has just received, but they were really still at an age that this had to be /taught/ to them: expecting them to have a whole thought process of "These bracelets belong to Birthday Sister, she just received them from OP, it would be rude to ask for them", is a bit much.
Very small children will ask for whatever tickles their fancy, and will happily accept it when it is offered to them.
So it wasn't really that horrid for the little ones to ask and accept. It was up to Birthday sister to breezily say: "Yes, they're beautiful aren't they? But no, of course I can't give them away. I just got them from OP, they're my present!" Contrary to what some people (in general, not any posters in this topic) seem to think these days, little children understand "No" very well.
And yes, if Birthday Girl was going to be so clueless about it, it was up to the parents to say: "Come now, girls. We can't just go around taking Birthday Girls presents from her. OP gave them to her, to have and enjoy!" And I might, just might, have said the latter with a pointed look into Birthday Girl's eyes, with a hint of "Are you crazy??" Heck, if I was the parent, I might even add "Imagine how you would feel if you had given Birthday Girl such a lovely present and she gave it to someone else! That wouldn't feel very nice, would it?" (What I would really mean with that, would be: "Birthday Girl, don't set such a horrid example of being boorish about gifts in front of my children!")
Disclaimer: I don't even have any children, so this is all very hypothetic. But it's along the lines of what I, as a teacher, would do in the classroom if Child 1 tried to give away a gift that Child 2 had given her to Child 3).