Olivia is irrelevant. She was a friend of Horace's, perhaps a lover, who was in his car with him the day they found the Linus family. She later moved to the island where she was the school teacher. She would have had a bigger part but they couldn't get the actress back. There was nothing stated in The Man Behind The Curtain that states Horace and Olivia are married. It was from a call sheet...which often have incorrect or misleading information. In season 4 we assumed Horace meant Olivia when he talked about the missus. Now we know he meant Amy.
What appear to be wedding bands are seen on left ring fingers of Horace and Olivia when they pull over outside of Portland to help the Linus family in "The Man Behind the Curtain". Horace and Olivia were probably married at that point in production but that changed in post-production.
Olivia was Horace's first wife, who left the island at some point between 1974 and 1977 -- possibly for reasons related to Horace's feelings for Amy. They divorced, Amy became Horace's second wife, and Olivia kept a low profile back on the mainland.
Olivia was part of an abandoned storyline.
Olivia (Teacher) was a cover identity for Karen DeGroot (with her husband Gerald DeGroot pretending to be Horace Goodspeed) so that she could spend time with the children on the Island to see if they displayed any special abilities. Under this theory, fake actors would have been hired to "play" Karen and Gerald in the Orientation Film to allow them to go undercover on the Island.
Based on the Mysteries of the Universe tapes, we know Olivia left the island. Is it possible that they are one and the same? Making Kate possibly Annie, who also left the island with her mother (possibly Olivia)? The age difference not being what we would expect is no more confusing than Charlotte's differing birthdates. Perhaps this would explain why Diane is living longer with the cancer than predicted.
The way that Olivia would have factored "significantly in the future 'game plan' for Lost" will now be handled by Amy.