It's possible that Sasuke was with Karin first and then Karin dies, and he falls for Sakura right after who mothers Sarada as if she were her own.
Karin maybe Uzumaki, but not all Uzumaki have Senju in lineage. Hashirama and Mito had kids, but there were still other Uzumaki, Karin can be Naruto's cousin through another Uzumaki that never had Senju blood, Uzumaki clan was killed off in the land of Eddies while Karin was alive, her village was destroyed (Not 100% sure) and the survivors scattered throughout the globe.
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not sure if wiki is 100% accurate