Demeter isn't in The Odyssey, but Persephone is the wife of Hades, therefore the Queen of the Underworld. Also when Odysseus travels to the Underworld, and finds his mother, she mentions something about Queen Persephone.
If you are talking about Mythology then Demeter was Persephone's mother. Zeus was her father.
Persephone did return to spend half the year on Earth between her mother, Demeter, and then to the Underworld to be with her husband, Hades.
In the myth of Persephone, the climax is when Persephone is abducted by Hades and taken to the Underworld against her will. This event triggers the conflict between Demeter and Hades, leading to the negotiation for Persephone's return.
There was only one child between Zeus and Demeter, and that was Persephone.
Three things; Persephone kidnapped/rape Demeter wrath on Earth Demeter finds Persephone, and must give up her daughter between autumn and spring.
Zeus sent the god Hermes to intervene in the myth of Demeter and Persephone. Hermes acted as a messenger between Hades and Demeter, helping to negotiate Persephone's release from the Underworld.
Loss and love: the loss of Persephone from the Earth goddess Demeter, the love of Hades for Persephone, the love of Demeter for Persephone.
In Greek mythology, Demeter did not have a romantic relationship with Hades. However, she did confront him when he abducted her daughter Persephone to the Underworld, which ultimately led to a compromise that allowed Persephone to split her time between the Underworld and the surface world.
In Greek mythology, Demeter is the goddess of harvest. Her daughter is Persephone. Hades is the god of the underworld and he kidnapped Persephone. To make a long story short, there was an agreement made between Hades and Demeter to share Persephone. When Persephone is with Hades, Demeter is so sad that nothing will grow and that is why winter happens.
Hades is the brother of Demeter in Greek mythology. Demeter is the goddess of the harvest and agriculture, while Hades is the god of the underworld. Their most well-known connection comes from the myth of Persephone, who is Demeter's daughter and becomes Hades' wife after being abducted to the underworld.
Demeter mourns her daughters lose every year, and winter comes to the earth. Persephone must go between the realm of Hades and the earth every year. Hades either must await Persephone or is with her.
Persephone once lived with her mother, Demeter. However, she was abducted by Hades. After an altercation between Demeter and Hades, it was decided that Persephone would resides with Hades for 3 months of the year. The other months of the year she lives with her mother.