Respect is always shown to the deceased as well as toward the mourners. This is one of the reasons why Traditional Jewish funerals are held so soon after death. It is more respectful to inter the body within a reasonable amount of time rather than having an unnecessary delay. Of course, waiting for relatives to come from a far distance is a respectful reason to delay the burial. This is a decision the family should make in consultation with their rabbi.
A mourner in Judiasm is one who is defined as being Kaddish related, which means they are obligated to observe the rites of mourning for the deceased. Those who are considered mourners are the spouse, parent, sibling or child of the deceased. It's important to realize that other family members, although not technically considered mourners, may choose to observe many of the rites of mourning because of the close relationship they had with the deceased.