The Question is not Rick Santorum but his father when did he become a US citizen
Not relevant. Santorum, having been born in the USA, is entitled to US citizenship by birth, regardless of his parents. Therefore, he's as natural born an American as Billy and Bernardine and fully eligible to be President.
Arguing this point is fruitless: the Court is never going to go the Vattel route. Even if they did, they don't have the authority to remove. That takes two thirds of the Senate. So, all you accomplish by bringing it up is to restrict the GOP field. That's pure stupidity! A total dead end! Marco for VP!!