In my humble opinion, only the first sentence makes sense. In the first sentence, Putting on my coat is an adverbial phrase modifying the rest of the sentence. In the other sentences, it doesn't modify anything, having no genuine connection to the rest of the sentence. The first sentence could be restated as I am putting on my coat, and then I am heading out the door to meet my father. In the other sentences you are talking about two separate actions that are totally unconnected in every way.
Originally Posted by jwschang