Meh..in my opinion the sage was Uzumaki..or atleast part..its not said which comes first out of the three clans, all we know is that Uchiha and Senju are the descendants of the Sage's sons..we don't know much about what clans are the oldest or which ones were around back then..(besides Uchiha and Senju as they came after the Sage)
It was stated in Naruto (non shippuden) near the exam time that the Hyuuga were one of the oldest clans and were distant relatives to the Uchiha. It doesn't say if the Uchiha came from the Hyuuga or vice-versa..but the fact that its stated as one of the eldest clans, the fact there is 2 branches because of a "traitor" in the past..
Because of this my assumption is that a Hyuuga member left the clan for there lover (someone outside the clan..as just like Uchihas the Hyuuga practice inner-breeding to keep purity) and the lover was probably Uzumaki or what would become Uzumaki, out of this union was born the So6P..which led to the Uchiha(Hyuuga/Rinnegan) and Senju(Wood/Uzumaki)
This is what caused the Hyuuga Clan to have a Main branch and Side Branch, the Side Branch are the descendants of this traitor who bred outside the clan.
I think its safe to assume the Hyuuga are one of the oldest clans and is probably the first Doujutsu..which is why its "weaker" then the sharingan/rinnegan, out of a union forbidden by the Clan between Hyuuga and Uzumaki or what would become..you get the Rinnegan/Insane Chakra/Impressive Sealing that the So6P gained, an evolution of both the Hyuuga's eyes and Uzumaki life force..then when the Sage had children that blood was thinned again to become Senju and Uchiha, both still improvements over the original parents of the Sage, but weaker then the Sage because of impure bloodline(The sage was the first of his bloodline, no one to purify with)
Also the fact that now we know the Uzumaki had some kind of connection to the Shinigami tells me they are a very old clan, like the Hyuuga..
So I don't look at it as a seperation from the Senju, I look at it as one of the Sage's parents was Uzumaki, which makes the Senju related to them and the other parent of the Sage was Hyuuga, which makes the Uchiha related to them.
In other words if Naurto and Hinata had a child, by my theory it would be possible the child to be born with Rinnegan and insane life force/chakra but if that child had children..unless he bred with a Hyuuga to purify the eyes or an Uzumaki to purify the body the outcome would be the same as in the past, one child would have a weaker version of the Rinnegan (devolved over time to Sharingan) and the other a weaker version of the Uzumaki life force (devolved over time into Senju)
Its like a giant loop that repeats itself, thats how I see this story coming to an end.
