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They didn't call her Tsunade Senju
The wiki isn't canon but since you decided to use it as an example anyway I'm going to use your own evidence against you.
1. The 2nd sentence on the page says:
"She hails from the village's
Senju clan, and is also a descendent of the Uzumaki clan through her grandmother Mito"
2. The bio under her picture lists her clan as the Senju clan. If she weren't a senju, the wiki wouldn't list that as her clan.
It's always sad when people don't bother to look at their own evidence carefully.
Also your logic is flawed. You said you feel like her mom is a senju but her father is not and since her father isn't it gave her non-senju like traits which makes her not a senju correct?
So does that mean that Naruto isn't really an Uzumaki? His mother is an Uzumaki (like you said Tsunade's mom was a Senju) but his dad isn't an Uzumaki. And Naruto's element is wind which he got from his father, not his mother. Naruto also isn't good at fuinjutsu which is an Uzumaki trait. So by your logic that makes him a non-Uzumaki correct?