Although I don't believe the brother had rennigan
I'm pretty much convinced hagoromo and the 2nd sage had Byakugan as well. Here's how I believe it all went down:
Kaguya, as a moon goddess, possessed the Byakugan before she ate the fruit. In fact, this may be why the Byakugan resembles the moon to begin with.
When she ate the fruit, she gained her third eye, the sharingan.
She gave birth to twins, both who possessed the same eyes as her, the Byakugan.
Kaguya developed the jyuuken fighting style and taught it to the two sons.
The two sages used this fighting style, as well as sealing jutsys they'd developed, to fight the juubi.
Once the juubi was sealed inside hagoromo, his Byakugan mutated due to the juubi into the rennigan. this is why the rennigan looks like a mix of Byakugan + Sharingan. Hagoromo then passed this new eye onto the Uchiha and his new body onto the senju.
But since the 2nd sage didn't become a juubi host, his Byakugan and body remained untainted and the same as his mother's, Byakugan was passed onto the hyuga while his body was passes onto the uzumaki.