There's a children's book with this title written by Methodist pastor Keith Tonkel. As best I can tell from the blurb and the preview on Amazon, the red and green doors symbolize the two ways in which children may enter a family: birth and adoption. The blurb says only that "Author Keith Tonkel explores families, adoption and being chosen in this delightful and meaningful children's book," and this is an excerpt.
Then Mike said: "And I'm glad that you are my sister, Jessie. I always wondered what it would be like to have a sister, and now I know. It's good when you can have a sister. Not everybody has one, you know.""I know," Jessie replied. "What you said was really nice, and I am very happy that you are here. I remember the very day when you came in through the green door over there.""Well," Mike went on to say, "Mama told me all about your coming in through the red door, and that's good, too. But what is even better is that we have both come into this house, this room, and have become this family."
Jessie remembers the day Mike came in through the green door, so she was already a member of the family when Mike joined it. But Mike says he always wondered what it would be like to have a sister, which means he didn't originally have a sister. Therefore, Jessie was born into the family (the red door), and Mike was adopted (the green door).
Jesse means "God exists"; Michael means "Who is like God?"