The sentence in which the underlined clause is a noun clause that functions as the object of a preposition is: Veteran trainers offer a great deal of love and discipline to (whatever dogs they train.) Option A is correct.
In this sentence, 'to' is the preposition modifying the noun clause "whatever dogs they train."
Noun clause is the group of words acting as a noun. They do not form a complete sentence, so that, these are dependent clauses and cannot stand alone.