Miranda Caliban is the mother of Friday Caliban. She is a resident on the Island. She lied to her daughter and told her that her father, Thursday, died during a storm when he was devoured by a manatee; the truth being that Thursday left the island but Miranda thought it was better to stay. Miranda did not want Friday to worry about the schism that divided her parents.
It is unknown whether Caliban is Miranda's married name or her maiden name, but either way she is in someway related to Olivia Caliban, whether blood related or through her husband. They may be sisters.
The name "Miranda" is likely in reference to one of the principal characters of Shakespeare's "The Tempest", a play concerning a group of people who are shipwrecked on an island. The play contains both a character named Miranda (the beautiful daughter of a powerful wizard) and another named Caliban (the hideous deformed son of a witch).
There is a theory that Mrs. Widdershins and Miranda Caliban are the same, meaning Fiona and Fernald are also her children. This would imply she was with Captain Widdershins who would be "Thursday" and had three children with him, but they broke up and she did not take his surname, nor did she allow Friday to become "Friday Widdershins".
Another theory is that if Olivia Caliban and Miranda Caliban are sisters, then it's possible they have a third sibling, N. Caliban, because of the alphabet name order of many siblings in the series such as the Snickets and Denouements. It would be MNO, as in Miranda, N, and Olivia.