"two children" is an unambiguous statement ... it can't mean one child, it can't meant three children, neither can it mean two dogs.

"one of whom" can be ambiguous ... it can mean only one (of the children), or just the one I am describing. Nowhere in the original statement is it said that the second child was not a boy born on a Tuesday. You can argue it's implied, but it's not stated.

Just because you say that the first child was a boy born on a Tuesday doesn't mean that the second can't be the way the statement is worded. This is a mathematician using English badly to prove his point!