I can't tell by your description. Was the elbowing intentional? Things do happen during playground play that are upsetting and even injurious but not intentional. If that is the case, then I think you just need to let it go.
For the rest of it, it is a tough situation. Can you tell if your DD is trying to prove to the other children she can tough it out, to you, or to herself? If to herself, then I would probably support her in that. If to you, then you might want to have a serious conversation about alternatives and how you wouldn't be upset if she chooses them. If to the other kids, that I understand. BTDT at about that age. It was important that I prove myself "stronger" than the bullies. Mostly for myself but also as a way to get them to back down without resorting to being equally violent. DIdn't work as well as I had hoped, but it was a good thing to try.
What has the teacher said/done? You say you like her, but it doesn't seem like she is effective. What has the principal done/said? Seems like he or she needs to be much more involved in the situation then so far. Even he or she can't keep your child safe, then escalate up the chain. Bullying is generally considered a very serious issue now, so you have current trends on your side. You should be able to get everyone's attention and demand they keep your child safe.
For the rest of it, it is a tough situation. Can you tell if your DD is trying to prove to the other children she can tough it out, to you, or to herself? If to herself, then I would probably support her in that. If to you, then you might want to have a serious conversation about alternatives and how you wouldn't be upset if she chooses them. If to the other kids, that I understand. BTDT at about that age. It was important that I prove myself "stronger" than the bullies. Mostly for myself but also as a way to get them to back down without resorting to being equally violent. DIdn't work as well as I had hoped, but it was a good thing to try.
What has the teacher said/done? You say you like her, but it doesn't seem like she is effective. What has the principal done/said? Seems like he or she needs to be much more involved in the situation then so far. Even he or she can't keep your child safe, then escalate up the chain. Bullying is generally considered a very serious issue now, so you have current trends on your side. You should be able to get everyone's attention and demand they keep your child safe.