OP, well you don't need to look very far to see Alice has got her bullying tendencies from!! An apple really does not fall very far from the tree in this case.
This mother is not 'sad' or 'embarrassed', she is making sure she gets her own back for your 'indiscretion'. She has her dd's back at all costs, even when she is hitting other children, and she is making sure you know it. She is trying to exclude you, and to make you feel so damn uncomfortable (and so far succeeding as you have described feeling punished by her)
Op:
This woman is definitely NOT your friend
This woman is a player of the worst kind - she knows just how to manipulate and hurt others. Do not be drawn.
Any decent parent, would have been mortified that their child had done this to another child, what you would have expected to see is a profuse apology, perhaps a sorry card from the child, and a parent addressing the fact their child is bullying another. But that is definitely not going to happen.
The only thing you can do is be bright and breezy, and do not let this get to you. Don't involve others, make no comment whatsoever. If she is blanking you when you say hello, just stop saying hello, and just go about your day as if she isn't there. Continue to support your dd with new friendships, focus your energies on play dates for her. Stay in contact with the school about the bullying, and keep monitoring the situation with your child. The other mothers will soon work what she is like, so leave them to it.
In the meantime if you have other friends, look to spend more time with them for support and fun.
Rise about this, do not cower away and feel embarrassed, be strong and confident, walk in and out of school with your head held high talking to the kinder mothers as you go, and your dd will learn to do the same.
No one gets away with doing this to your child, this is a perfect opportunity to show your dd how to be strong and resilient.
This will blow over, do not give it your time or energy.