Your translation have a different context, which tends to refer to a physical object. Eg, "the ball is in between you and me". The "in" is redundant, but not technically wrong. However when talking about personal matters or intangible, there should never be an "in" before between.
No, but you can say "det där är mellan dig och mig," however that seems like it would mean something specific, whereas simply saying "Det är mellan dig och mig" could mean that whatever "det" refers to in this sentence is a secret. I don't think "det där" gets that same message across.
Did anybody else think mellan sounded like mellon (lotr elvish for friend)? (I'm such a nerd!)