What if the Hyuga and Uzumaki were the result of the senju and uchiha coming together? I kinda doubt it but it's just one of those random thoughts.
I would, actually, argue that the opposite is more likely.
The Hyuuga and Uzumaki predate the Senju and Uchiha. The theme of the series has been history repeating itself with the successive generation surpassing the former. Naruto - an Uzumaki - has already been compared to the Sage of Six Paths (foreshadowing).
Neji was always rambling on about Destiny and how his was to protect the head clan - which was fulfilled. And what is Hinata's destiny?
To fill the supporting role to the next Sage - just as a Hyuuga did eons ago.
It was the Uzumaki and the Hyuuga who gave rise to the Uchiha and the Senju through the Sage, the Juubi, and his wife.