The problem is that the prose in the middle is stage business, and there are only so many times you can interrupt with stage business. I think you have to punctuate the non-dialogue bits as sentences, not interrupters.
“Dawn once told me about a problem she once had with her step-mother." Wendy cast a furtive glance at Dawn, to check that she was allowing Wendy to continue. "The one where she found her step-mother..." She reduced her volume considerably. "...with someone who was not her father."
The continuing dialogue can have ellipses and dashes and whatnot to indicate that the speaker hasn't actually stopped speaking, but I'd be hard-pressed to think of an example where you can interrupt with prose more than once.
ETA @what actually gives a decent example, although I note in my comment that it only works if the entire piece is structured in the same loose way.