It's not a horrible concept, but I don't think that Raava has it in her to split herself in two, especially in the event that Korra can't leave the world in enough balance to facilitate such a division of self and power.
I thought it would be a set of twin brother and sister, the mother and fathers identity unknown, the older twin brother water tribe like the father( but this won't be discovered until later in the series) and the mothers origins are earth kingdom (obvi) and located in kiyoshi island! (And was a kiyoshi warrior until her family left the island when she was twelve)
So the younger sister was the avatar! And because they are orphans the brother was sadly adopted to a family without her, and she made her way to republic city with some friends .
I wanted the avatar to be a girl to redeem the fails of Korra.
Anyway, so Vaatu has taken the body of an air bender and died with Korra, she died in her early 20s and now has a fire nation host. (A reverse cycle to the avatar)
So mako is the fire bending master to the new avi, bolin is a big time mover star and married to a songstress. Asami is doing her business stuff. Ect.
And that's all I could decide on.
It would start off with Korras death scene as the new avi wakes from the visions of this, and nobody beyond Korra and the mystery air bender, and his/her followers, whom by the way, take vaatus host body away, thus nobody knows who is responsible for killing the avatar.
This upsets everyone and they fall out of touch. Mako has insomnia, Bolin is constantly on the next big mover to avoid dealing with the loss of Korra. This is also Asami's method of avoidance.
Nobody knows about the identity of the new avatar, so she is just your average 19 year old metal bender cop. Clumsy and naive, but still a capable cop. Has a love interest, but when ever he comes by she can't say anything, so he thinks she's a snob.
It needs a lot of putting together, but this is my idea.