nah uzumaki and senju are explained like this.
Mother has two children, boy ( senju) and girl ( senju), boy keeps base senju name.... girl marries into another nation or line( uzumaki)
now boy has son...Senju.... girl has son ( uzumaki )
( uzumaki) apparently has a blood limit combined with Senju, thus all uzumaki's who breed within pool have red hair. Tobi/madara manipulated Nagato as a child, or stole him.inserted the rinnegin and sent that pup to the rain village.
now the question is, what the hell is the fourth( senju line?)
Nope, Senju's wife was a Uzimaki, they are both descendants of the six path son who didnt get the eye ability. Uzamakis have a longer life span and more stamina than regular ninjas which is one of the traits they got from their ancestor, thats why they are good candidates to host the tailed beast like Naruto's mother and the first hokage's wife who is naruto's grand mother



