ANSWER - Modern Pagans often refer to death as the crossing of the Rainbow Bridge - the Rainbow Bridge being a spiritual place where the pet awaits its owner before they journey to the afterlife together. The origins of the allegory lie in Norse Mythology and the bridge that spanned the distance between Earth and Asgard - the home of the Norse Gods. It is not uncommon for a pet to hesitate to cross the bridge or for the spirit of a pet to linger after the physical form has died and there are a couple of different reasons for this. In the first case animals do not always realise they have died and sometimes try to keep their relationship with their owners and their home the same as it was when they were alive. There can be bewilderment within the pet as to why the owners are no longer interacting with it and this can lead to the spirit becoming confused and unable to cross over.
Some pets do not want their spirit to cross over because they do not want to leave their owner. This can often be the case when the owner is grieving and the pet wants to stay behind to offer support and love. In these instances the spirit of the pet often finds a peace as the grieving fades and little action is needed as the spirit will quietly pass over when he/she feels the time is right.
Often a spirit will choose to remain for just a short period or it will visit the former home once or twice before choosing to pass over of its own accord. This happened to my mother with most of the dogs she ever owned, they would come back as a brief physical manifestation, almost as if to reassure her that they were content and safe before crossing permanently. Again if this is the case you will find you need to do very little, the spirit will be aware that it cannot linger.
In terms of how to actively help the spirit to cross the first thing I would recommend that you do is to make it clear to the dog that it has died. Performing a short ritual in the house or garden would be of great help here. Physical remains need not be buried in a formal burial ceremony but you might like to bury something symbolic such as the dog's favourite toy, water bowl or other personal item. Address the ceremony to the dog and make it clear that this is the family saying goodbye. Explain clearly that the dog's spirit is free to continue on its journey and does not need to stay with the family.
There certainly are magical steps that you can take. I would suggest a cleansing of the house - a simple smudging with sage would do. I'd also suggest you house the spirit away from the home. This would be best achieved if you do have some part of the animal (the ashes from cremation would be ideal) but if not you can incorporate into the burial ritual with the favoured owned item. Hold the chosen item/ashed and ask the spirit of the dog to inhabit it. Place the item in the earth and bury it while visualising the returning of the body to the earth and the freeing of the spirit. Be clear with your words- tell the spirit of the dog that you are setting it free.
When you have completed the ceremony it would be worth completing a prevention smudging to deter the spirit from returning. I would probably use some Cypress incense to smudge the boundaries of your property.
I wonder if perhaps the owner's daughter's dog is picking up not just on the spirit but on the anxiety of her owner. It might be worth discussing the nature of spirits with her and explaining
that the spirit has not remained to frighten her but it has remained through love of the family. If you can reduce the fear that the spirit is malign (which it definitely isn't) you will reduce the anxiety in the family and the spirit - sensing peace - will feel it is less needed for the purpose of protection, freeing the spirit of the dog to leave the family and cross the bridge.