I'm not suprised that a compromised and vulnerable 10 yo has physically lashed out after 4 verbal warnings by her and OP failed.
The problem with a gentle, nicely, nicely approach to life is that very occasionally being nice and reasonable is never going to work with some people who can cause you harm. Reason should usually be the first port of call, but if you are threatened, you should be able to defend yourself appropriately and the law is relative to situations, not absolute.
At 16, at the bus stop, the bullies trying to drag me to the ground had established history of ignoring reasoning to leave me alone. They got physical, so I responded in kind. I didn't bother with pointless niceity that time, just unhooked my shoulder strap off my bag, let it drop under the bully's and its own weight, and as a lovely bonus, the metal buckle swung round and cracked her on the nose. The bus turned up as she picked herself up and she shouted "what did you do that for?" My response was "you deserved it!" They never went near me again unlike all the times I ignored them or told them to leave me alone.
In my twenties, I woke up and realised I was being sexually assaulted by an aquaintance. My reaction was to kick him in the face. Hard. I bloody well hope it hurt. That kick may have saved me from rape.
Obviously a 6 yo is below the age of criminal responsibility and being a rude nuiscence rather than the more serious descriptions that would be applied to adults displaying the same behaviour. However to a 10 year old who has a need for privacy, that is little comfort.
As an adult in this situation, I'd probably get down to the child's level and talk close to their face which tends to have a different impact to shouting, but OP's DD doesn't have that extra life experience, and long experience of working with children.
The 6yo should have been appropriately supervised, not AWOL and able to get into that position. Although the natural consequences stance is something I'd share with my DCs when one has been particularly antagonising or immune to reason. If DS1 in particular (ASD) has been excessive with DS2 (9&6) we talk about how the situation could have been managed differently. Getting cross with him when he feels wronged and has been unable to cope or mask any more gets us nowhere.