This is what I think tell me your thoughts:
I do believe the Sage was Uzumaki (100% Senju) and when he died his hair turned white like Nagato's
There's no way Uzumaki has Uchiha within them because Naruto would have Uchiha skills if that were the case (which we know isn't)
The sage had become the Jinchuuriki of the Juubi, and from the Juubi, Influence on Uchiha could be born
I know this because i already stated this and so has another person i am talking to on this thread your merely repeating what has already been posted on here if you are not caught up on the pace of the conversation read pages 9 -12 to get the sum of it,that is where most of the noobs left so people with an actual opinion on the subject could talk without their post being separated by rubbish.Anyhow you seem to get the relation between all three so far.
uzumaki(sage) takes in bijuu and at that point become one then the sage has two sons one gets his yin nature the other gets yang nature the power of the sage is then split between them with the uchiha taking on characteristics of the bijuu while the senju ancestor takes on characteristics of the sage himself which is why the senju and uzumaki seem to share a deeper connection
but if i were to break it down into specifics it would go like this
the uchiha ancestor manifest the spiritual chakra into his eyes the yin nature while taking on juubi traits while the senju ancestor take on the life force (yang nature ) and traits of the uzumaki out of the three traits the senju took two with the uzumaki retaining the longevity.