When your kids hurts another kid

So my daughter and another dcb got into a fight over a toy. I stupidly got involved and sided with dcb and my dd got made, pushed this kid and he fell onto a doll bed getting a welt on his face.

She was consequenced (she had time away from group, met with dcb and me to talk about what happened, apologized, we read a book about managing angry feelings). I sent an email out to his parents explaining what happened and what I did about it. I was also transparent that this can be a potentially awkward situation as she is my kid and they may to feel comfortable talking to me about it but invited them to do so. Should I do something else?

My dd and this dcb have been having a hard time with their relationship the last 2 months/ I was hoping the holiday break would help but it doesn't look like it has. I now have another dcg who is also 3 (started after the holidays) and another dcg pt. My dd in particular feels very threatened by these girls when they play with dcb. He now has other options when my dd is mean to him (good, she needs the lesson) but I am at a loss as to what to do. Suggestions welcomed.

It's always hardest with our own children when we do home daycare.

Firstly, you did the right thing by removing her from the group, and reading a book about angry feelings. That's awesome! Don't feel badly or uncomfortable around dcb's parents. Your child is part of the daycare and is also learning social rules and boundaries, just like the other children in your care. You did not show any favoritism and you explained the outcome to dcb's parents.

Some children, like adults, don't mesh well together. Dcb and your daughter could just have "outgrown" their friendship and now view each other as rivals of sorts. I would up the structured activities. Break them up in groups of 2 when pt dcg is attending. So when doing crafts, or puzzle or whatever activity you have set up, allow them in their groups and then rotate groups. Praise your daughter when you see her interacting well with dcb (and the other girls).

I would also keep a closer eye on dd and dcb. Maybe hang back and just watch them closer during freeplay so when another tug of war occurs over a toy (and it will) you can intervene before it gets to heated. I'm guessing your daughter is 3?

I can totally relate. Not that I will have a lot of suggestions as I am going through the same thing here.
Of course it feels much worse when its your own child as the one inflicting the damage.
I have a dcb who started first in this group I have, he was the one who was first to walk as well, he would go after my son in particular who was not walking at this point and just constantly went after him, snatching toys, biting him and knocking him down etc. I kept thinking to myself wait until my son starts walking. Well once my son started walking he seemed to remember the treatment this dcb gave him and for a few months just went after this dcb. It was like soon as I put them into the playroom and shut the gate "ding ding ding" like a wrestling ring or something. It has since stopped with ALOT of timeouts, redirection and direct supervision when the two boys were in the same room.
Could you take your dd and have her do something else with you as soon as you sense conflict with the other one(s). Have her help you get snack ready, and hand it out etc?