Hi John,
It's probably best to speak with your niece. Surely, she would want what is best for her mother and would be willing to accept financial and emotional help from other family members. The legal route is cold, impersonal and could damage family ties. As for how long to leave a body at the morgue, can you call them up and ask how long a body usually remains there for?
As for funeral arrangements, you could try calling up a funeral parlour and enquiring as to who can arrange for a deceased person. A personal representative usually arranges the funeral, but this may not always have to be the case. A funeral parlour should be able to help you out on this question.
A personal representative (appointed by court), and nobody else, can administer the deceased's estate, though. A child over 21 will have priority, however, any eligible person (parents, sibling) can apply to court to be a personal representative, but court will need to "pass over the person" with priority (your niece). However, this may not be necessary for funeral arrangements.