Chloe, my heart has broken for you. I understand what you are going through. Our cat got bitten very badly from a snake just after Christmas last year. After 18 hours intensive care & drugs, she died. We had 2 weeks to pay off a $1200 account.
Our little man, approx 2 1/2 at the time, took it really hard. He used to play with the cat daily, they had their own games & she would seek him out to play. She was a guard cat for him when he was born, was with him more than she wasn't.
Our son was at my parents one day & he found a little, stuffed, black cat. He named it after our cat & still doesn't sleep without it. He talks about the cat quite a lot, even now. It has helped him to deal with his grief.
She is buried in our front yard & there is a cat statue next to her grave. This has helped too, as he talks to her & knows where she is.
It will take your children time to grieve & deal with their feelings. Maybe ask your 9 year old if he'd like to choose something put on the grave as a memorial. Have a gentle chat about what happened & how he is feeling/coping. It will be hard & don't hold back from showing how upset you are either. Tell him it is ok for him to cry & let his sadness out.
And if that profile pic is of your precious puppy, I'm even more sad for you. They are my fav breed. (I lost mine to a brain tumor when she was 6).
Take care Chloe & family & huge hugs to you all xxx