All of these responses are normal and healthy. Showing your own grief in front of your child is healthy as well. Hiding grief might make children wonder why you don't miss the presence of the pet in the house. This could lead to them wondering if you would be sad if they died. Grieving and crying in front of a child validates to the child that these emotions are OK to express.
Families can be creative about memorializing their pet.
Plant a tree. Put an engraved stone in your cat's favorite spot in the house. Write a letter to your dog. Encourage children to draw pictures. 244-CARE for hours of operation.