This isn't a child friend issue... it's Amy's parents that are the issue. In that they don't. Parenting her is, apparently, too difficult for them from what you've explained. Now that she's old enough to have emotions and act on them; realize that she doesn't HAVE TO obey; knows that there won't be any consequences of value; her parents have given up; this is all she knows. She's acting out begging people to pay attention to her and love her and give her boundaries.
Her parents have given up because of the monster they created by giving in and likely, not correcting certain behaviors when she was very little because they were cute. Now that she's older and the behaviors aren't so cute, everyone including her parents just expect her to know better just because she's older.
I'm sure she also has splendid examples of how to behave appropriately at home (sarcasm there, folks).
This won't stop with this unfortunate little girl unless her parents take parenting classes and shape up their parenting. And that means that at this age you have every right to help your daughter choose her friends and if that means telling her she can't be friends with someone then you do it. This is a situation where I see no point in forcing your daughter to be the other girl's soothing blanket and it's no time to teach your daughter a lesson in compassion and looking for the value in a challenging friendship.... because this isn't a friendship.
If the girls are in the same class and the bullying is this bad already then I think you have cause to request that your daughter change to another classroom. You can't ask to have the other girl removed because they can't honor that request. It would have to be your daughter moving.
I would also NOT allow your daughter to walk home with this girl because it's putting her, a little 6 year old girl, through the longest most miserable walk of her life day after day after day. That's torture. Find another way to get her home.
Absolutely encourage your daughter to speak up in self-defense and in defense of others, but avoiding the situations when possible at only six years old is best. This little, she does need protection. That other girl's parents aren't helping and trust me... as a girl who was bullied and always in my bullies classes because my mom never thought to ask to change classes, I would have welcomed simple solutions like that. Out of sight, out of mind.
And yes, no more play dates. Period. None. If you have to tell her parents straight out why, then do it. Hell maybe they'll tell the child why she's lost a friend.