Do not be concerned about allowing your children to be present during any funeral service or during an ash-scattering ceremony. The death of a pet is usually the first experience a child has with death. It should be as informative and as free of stress as possible, especially if the child was very close to the pet.
As all pet parents know, a pet's life is limited. When in fact the time comes for your pet to pass on, you should know that there is a place for you to put them that they will be protected as well as remembered. Many cemeteries are providing these services to you. You can also look for local cemeteries that are dedicated solely to pets.