Yes, as long as you don't put another noun in between. "I looked over and saw a dog barking while driving through the neighorhood." - implies that it was the dog that was driving.

Your example is perfectly all right, as Maxey pointed out very well. Another way to write the sentence is as follows. "While playing in the street, his daughter was run over". This wording places the most important action last, thus serving to emphasize it.