Is the underlined participial phrase correctly placed or misplaced?

continuing to stir the soup, the phone rang and my mother answered it.

underlined words: continuing to stir the soup

a.
correctly placed participial phrase

b.
misplaced participial phrase

The underlined participial phrase which is "continuing to stir the soup", is placed incorrectly. The correct sentence should be, "The phone rang and my mother, continuing to stir the soup, answered it". Why is it misplaced? Putting the participial phrase at the beginning of the sentence makes it a dangling modifier because it does not clearly state the specific word it modifies. In the corrected sentence, it is clear now who is being described with the phrase "continuing to stir the soup", which is the "mother".