Does the statement "Your daughter, I have divorced her," intending to inform, followed by his saying to his wife, "Now relax, you are divorced now," constitute a second divorce, given that he only intended to inform about the first divorce?

If you intended to inform of a previous divorce by saying "O divorced one, you are divorced" and did not intend to initiate a new divorce, then that is not considered a divorce. This is the more correct view, especially if she was in her revocable waiting period ('iddah) and you had not yet taken her back.