Hello Scott, I'm your worst nightmare! No, not really, I hope anyway that I'm not classified as an idiot with a rebel that calls himself a pro (because I neither have a rebel, nor do I call myself a pro).
However, inadvertently, I do take away some of your business because I price low since I have a day job and I do photography for fun. I could go completely free as a matter of fact, but I charge for three reasons: a) so that I don't create the "free photographer" reputation, b) so that I offset some equipment, and c) out of respect to you. Yeah, I'm not into the business of destroying your business.
Anyway, I have some advice for you as to how you can explain to the customer that you are better than me.
First, I don't have a real studio. I have lights, backdrops, props and stuff, but I convert my house into a studio when I have a gig. Show your high paying clients your studio and make a point about it. Somebody who's willing to pay top dollar would probably find my living-room studio a little stupid and your real studio more appealing.
Second, I don't have time to postprocess, since I have a day job. I do postprocess of course, and I do a lot of it, but that means that my clients have to wait for weeks before they get their pictures back. Show your client a before and after picture where you did magic in photoshop and tell them that they'll get this type of service from you and they'll get it fast.
Third, I don't have the volume of pictures to make any local printing store pay attention to me. Go to a local store and persuade them to give you a discount in return for doing all your prints there. Then offer the client complete solutions (albums, mugs for grandma, canvas, whatnot).
Fourth, I don't have time for photography all the time, so I have to squeeze my clients in my busy schedule. Offer them flexible scheduling and offer them to do things at their place, if they prefer (pregnant ladies like that, and so do parents of infants).
Finally, advertise yourself locally. Facebook might bring you customers, or it might bring you the wrong customers, but going to a maternity clinic and leaving a few cards with your contact info and a few nice maternity shots on them, could do miracles.