D..
Take pictures of them together. Let them say goodbye to the cat. Don't explain that the vet is putting the cat to "sleep". Do tell him that the cat is dying and needs help from the doctor because she's in pain. Don't use the word "sleep" in place of "dead". Children take things literally and will think that she might come back if you euphamize this. Don't take them to the vet with you. Have a loved family member or favorite babysitter stay with them while you are at the vet. I would not bury your pet in front of them or tell them that you have brought the cat's body home with you.
It's okay to cry about it in front of your children. If they ask if kitty is going to heaven, it's okay to say she is going to kitty heaven. Expect difficult behavior for a while. Be kind and loving, but still firm. You can say "I know you're having a hard time right now. We all are. But we still have to do "x"." That acknowledges your child's feelings and will help him figure out why he is upset when he might not even realize why.
When my kids wanted to pray for our dog, I let them and prayed along with them. That might help. (Let your child take the lead in that.)
I will tell you that my dog died about 6 months before my sons' great-grandma did. In a way, losing a pet beforehand helped my older child cope with the loss of his great-grandma. It kind of got him prepared.
So sorry about your cat - I know how much it hurts to put a beloved pet to sleep.
Dawn