Must I wait three years to propose to my cousin after she was proposed to by another suitor whose father was not present, but only his mother?

It is forbidden for a man to propose to a woman who is already engaged to his brother if her guardian has agreed to the first suitor, based on the Prophet's (peace be upon him) saying: "None of you should propose over the proposal of his brother."

However, if there was no explicit approval from the guardian, but rather silence or an indication of satisfaction without explicit declaration, then the second proposal is not forbidden. For the prohibition to apply, the second suitor must be aware of the first proposal and the guardian's approval of it, and of the prohibition of proposing over an existing proposal.

If he was not aware of that, or was ignorant of the prohibition, or if there was a rejection of the proposal from the guardian or the first suitor, then there is no blame on him. It is permissible for the girl and her guardian to annul the engagement whenever they wish.