I am so sorry. Putting an animal to sleep is one of the hardest and one of the kindest things to do. It takes putting your beloved pet's well being and comfort above your desire to hold them. There is no doubt that time is going to be their biggest help in dealing with the loss.
I have had to put one dog down. I knew it was coming, so that helped prepare me. But afterwards the thing that helped me most was talking about the silly things he did. I was laughing and crying at the same time. So maybe have everyone talk about their favorite memories.
Another is to look for signs that the bunny may send to let her now it is ok. Some people say seeing a cardinal is a sign of a some who has passed is checking in. Or maybe if the bunny liked munching on dandelions, one pops up . You know something that would be special to the bunny. The night after I had to put my boy Thor to sleep, Arabella and I were in bed and she started snoring. She NEVER snores. Thor ALWAYS snored. I knew that a sign that Thor was ok.
Hugs to you and your family.