No. Just no. A few points
The "oldest" clan title was given to them because the Uchiha and Senju were basically nonexistent at the time. The Senju and the Uchiha are the oldest clans of Leaf village because they were the founding clans.
The assumption that the Uchiha came from the Hyuga was just that, an assumption. If the Hyuga were descendants from the Sage like you say, then the Byakugan would be able to read the stone tablet that the sharingan and rinnegan can read. The Byakugan has not been stated or hinted that it can read the tablet. Something that eyes descended from the Sage should be able to do.
The Hyuga are in no way more peaceful than the Uchiha. The Hyuga allow only the first born of the main family to live peacefully. That means that one person from each generation, maybe two or three people at a time are the main family and do not have the curse seal on their heads. If the branch family, the mass majority of the clan, step out of line, then they can be put to death without hesitation. The Hyuga are ferocious within their family, more so than the Uchiha in terms of strict adherence.
The Hyuga may be descendant of the Sage but they are not closer than the Senju, Uchiha, or the Uzumaki. There has been no statements to the Hyuga being part of the sage lineage, and we are nearing the end of the manga. It is highly unlikely.