This is the first time I will have to show strong disagreement on all fronts. I am going to go point by point here:
- Lineage: Uchiha and Senju did not share any love and peace nonsensical rubbish the manga is feeding us through the likes of senju-supporters or Senju clan members themselves a la, Tobirama. If you remember clearly, Uchiha and Senju were nothing but mercenary clans who were repeated hired by several nations to shed nothing but blood. Sure Hashirama grew tired of it first, but Uchiha clan extended their hands for a truce such as readily.
Uzumaki clan being a clan of peace is nothing but speculation on your part. Take Nagato for example, he lives in the rain village, surrounded by fire, earth, and one more country that has just slipped my mind, and hence forth was always a battleground for wars. When Konoha bested other countries in the last great war, Nagato lost everything and after final intervention from Konoha, he became a figure-head of a renegade organization - nothing immoral about that, honestly - assimilating several powerful missing-nins.
Karin's origins are completely unknown. Mito was from this village, and so was Kushina. If I am to assume that after Uzushiogakure's destruction after the last great war - as the story goes - then at least Karin was from there as well, as people scattered after its destruction? According to the data, the village was destroyed for their fuinjutsus - sealing techniques - then they obviously utilized it during times of war, as their Funijutsus obviously would've been a treat to other villages. And since Senju clan had good ties with them through Konoha, there is nothing to assume that this village was also not present before Konoha was created, and its members participated as hires as well.
Cutting the long discussion short; none of these clans were peace-loving clans as you make it sound like.
- Kinship: False. It's easy to discern from all the given statements that the Uzumaki clan originated some time after the younger son's reign, as one of the family - Senju - members must have wed into another clan, predominately a powerful clan now lost to history, that gave rise to distinct features within the clan, as red hair and long life-spans. We all know that the younger son had the sage's body, hence if one of his offspring or near descendents wed another individual from another clan, it's highly probable that the biological or spiritual features of the Senju clan mutated and some traits over-whelmed the line, namely body energy - a distinct factor of Senju clan.
Even after the lines 'thinned' Hashirama's cells give indefinite boost to abilities, and we all know that Madara and Hashirama are closer to the older and younger sage's son then anyone else. Henceforth it's safe to assume that the younger son had similar body/chakra/biological features that carried on to and expanded from the aforementioned off-spring. It's called cross-breeding. That clan must have been like the Uzumaki clan to the younger sage's sons clan, which remains unnamed. And it's quite possible that through further marriage with that unknown clan, Uzumaki clan was born. You have to think of parallels here, as this manga had done nothing but 'repeat' scenarios.
- Rinnegan: I hardly doubt it. The manga clearly mentions that the two major clans started from older brother and younger brothers. The obviously wedded into different powerful clans, but since they were the sage's direct off-springs, their biological traits were hard to over-whelm. Uzumaki being an off-shoot from the Senju clan - as I explained earlier - has certain Senju traits, predominately the body energy, but they also carry the longevity factor, that was probably a trait of their original ancestor.
Nagato was given the Rinnegan, because he has an 'incredible' life-force and large amount of Chakra to handle the burden of the Rinnegan. It has also been repeatedly ventured that both the power of the Uchiha and Senju make up the Sanin. Adding both of them doesn't equal Uzumaki, otherwise, Karin, Mito, Kushina, and Nagato should have had Rinnegan by default, which were the sage's eyes to begin with.
I am afraid, I completely disagree, but it's a great theory. Kishimoto is known to create ass-pulls honestly. Who know. Good job regardless, as the matter is thoroughly researched, not musings of a fanboy. *****.