I think that as soon as Hinata has a child on it's third birthday then Hanabi would be sent to the branch house. Or all female after the first born stay in the Main house and are then arranged to marry Branch house males so that the Hyuuga blood stays within Hyuuga members?

So it's kinda like:

1st Born - Heir of Main House
2nd and other children born - Male- Branch House, Female - Main house

Then the Female from the Main house would have a child with a Branch house member and the child would stay in the Branch house. We've never heard a thing about Neji's mother so for all we know it could be true.