I recently had a conversation with my wife where I shared a hadith with her, which I recently came across, where it says, father has a complete right over his son & his sons complete financials.

Wife said, it’s not the case. Her sister in Saudia came to know that if both mother & wife dies at the same time, it’s sons duty to offer kafan to wife before providing it to mother.

Could you please shed a light on this. I also read that parents have more rights compared to the rights of wife & kids.

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This is just if the father is in need, and his son is not supporting him. In this case, he can take his needs from his son's money, with no need for permission.
With regard to Kafan, yes, if both died on same time, and he can provide only one kafan, then the wife is the eligible, not the mother, because the wife expenses are forefront compared to parents, while the obedience of the parents is forefront compared to the wife.