Is it the word "between", but truncated, or a portmanteau of "in between" and "teen"?
Here's Merriam-Webster's definition of portmanteau:
word or morpheme whose form and meaning are derived from a blending of two or more distinct forms (as smog from smoke and fog)
Here's The Free Dictionary's definition of tween:
A child between middle childhood and adolesence, usually between 8 and 12 years old. [Blend of teen and between.]
The OED says tween is short for tween-age, after teen. For tween-age, they say it's an alteration of teenage after 'tween (a form of between).
So, yes, tween can be considered a portmanteau of "[in] between" and "teen".