TaliZorah - I was advising that sharp-toned, blunt approach because the OP seems to think there are only two options - softly-softly, or lashing out verbally in temper at her niece.
I think that, if she does this each and every time her niece starts in on her dd, it will have some effect. Firstly, if she's shut down every time she starts, the niece might stop doing it. Secondly, if the OP is using a clear, carrying, sharp tone every time she stops her niece in her tracks, other people around will hear, and this may be enough to embarrass the girl's mum into finally stepping up and parenting this child properly.
I was horrendously bullied (verbally) all through the last year of junior school and all five years of secondary school - it stopped when we went to sixth form college, but the damage was done by then. My mum told me that I should just ignore the bullies, and they'd get bored and stop - 'sticks and stones would hurt my bones, but calling names wouldn't hurt me' - bollocks, mum!
I wish my mum had spoken up on my behalf - and I wish she had helped me learn how to deal with the bullies. This will sound utterly unbelievable - but I did not know the word Fuck, until I was an adult - my parents utterly disapproved of swearing - but I can't help wondering what would have happened if I had told the bullies to Fuck off!
As someone still suffering the effects of bullying in my childhood (depression, anxiety, low self esteem, suicidal thoughts - I was having those aged 14), I know how damaging bullying is. As the parent of a child who was bullied at school, I know how it is a knife in a parent's heart - and when I found out ds2 was being bullied, I took immediate action - but that action did not involve attacking the child concerned - with my rational adult head on, I could see that he was a victim of his upbringing - even whilst the tiger-mum in me was longing to let loose.
But dh and I did take action - and were prepared to take things as far as necessary. In ds2's case, it was happening at school, and they dealt with it swiftly, firmly and effectively - but we would have done whatever was necessary, had they not sorted it out.
When ds3 was bullied at the same school, we were ready to change schools, if the school hadn't taken it seriously again - which is why I am advocating that the OP cuts down on time spent with this little girl and her mum, if the parents won't discipline their child.
So, whilst I can understand why the OP lost her cool and lashed out, I know it was the wrong thing to do. As an adult, she should apologise for what she said, whilst being crystal clear that she thinks that her niece's behaviour is nasty, bullying behaviour and she will not put up with it any longer.