So sorry to hear this. Hope all went peacefully yesterday.
Get the kids to have a funeral of sorts - it helps them. Mine had one for a previous bunny and it was lovely. All their toys came and it was conducted by a meerkat! It really helped them and gave them a focus.
In the end we waited two days before having to put her down. This gave us time to nurse her and come to terms with it a bit. It was sad when the time came but the shock had worn off. We had a funeral in the back garden with flowers etc. DCs have coped better than I expected. They are already talking about getting a new one!