This book is about a young girl who lives in a magical town near a sea or body of water, where people have to go through a maze to travel to the outside world.
She has an older male companion (an uncle?) and they travel back in time with some of their friends to the Lincoln time period. He is also a stage actor in that time period along with his fiancée.
I read this book long ago, and I think it involves using some kind of merry-go-round or something to time travel.
I think that on the cover of the book is some kind of carriage.