I would like to know the exact word describing the relationship between myself and my daughter's father-in-law.
(not a professional teacher) As a native English speaker and student of Hindi, one of the things I most admire about Hindi vocabulary is its wonderfully precise and detailed vocabulary for family relationships. Sadly, English does not have the same range of words. So, just as English has only "aunt" and "uncle" where Hindi has a whole range of words for different sorts of aunts and uncles, English has no one word for the relationship you describe. The most concise term to describe a daughter's father-in-law in English is, "daughter's father-in-law".