oh sorry, to answer your question about how I reacted to DD1's behaviour.
The first times it happened, we tried to remain calm and teach her it is not acceptable. She did understand but would often need to be reminded.
Several times she drew blood and we realised that we were not being severe enough with her and upped our punishment, stronger telling off with a consequence - removal from room, put in corner or simply not being included with the other child's play.
We always made her apologise and offer a hug or a gift of some sort - a treat or toy.
It was not pleasant for us and it was extremely embarassing even though we accepted it as a developmental phase (and there were certain triggers we identified as well).
As I said below, I do not accept children hurting one another and feel they are never too young to be educated on it (age appropriately).
When DD2 was born we could not leave them alone at all because she was still demonstrating these unwelcome behaviours but we did work very hard with her CONSISTENTLY and we were happy to see the decline and eventually her full realisation that there are consequences to bad behaviour and that hurting others is not nice.
My other SIL used to discipline too if she saw it and I didn't and I was never so egotistical or proud to say that she couldn't discipline my child, she was only reinforcing the teachings that we were trying to instil in her.
If DD2 displays these kind of behaviours (less likely though as VERY different natures), I will deal with accordingly and will never ever find it acceptable for my child to inflict pain on others.
Hope that answers your question