They say that the Uzumaki are distant relatives of the Senju. How exactly are they related is up to speculation because it was never revealed. If the Uzumaki clan is a branch of the Senju, meaning that the Uzumaki Clan was created from the Senju Clan, then the OP is right.
But the possibilities of how the Uzumaki are related to the Senju aren't just limited to that because the Senju/Uzumaki relation has not been fully defined other than being listed as distant relatives. But what I can conclude is that if the Uzumaki are distantly related to the Senju. Then they are also distantly related to the Uchiha.
But the possibilities of how the Uzumaki are related to the Senju aren't just limited to that because the Senju/Uzumaki relation has not been fully defined other than being listed as distant relatives. But what I can conclude is that if the Uzumaki are distantly related to the Senju. Then they are also distantly related to the Uchiha.