I love this and may use it someday.
I wonder what this mom/former director is looking for, specifically.
I don't think I've ever been asked to have a parent sit in here. But to me, they get to see the environment during interview, and I do ask them to bring their child for the interview. If a child gets along well with other children, that is gravy. If they're wondering if there are any awful behavior problems, they can just ask. I talk about the other children (ages, genders) during interview. I put a lot of effort into teaching children to treat each other appropriately (if old enough) or managing the environment (if younger).
I recently had an interview for a (very) part time child where the mom wanted references. I gave her one to call and shared some other public info about another family. Then she wanted the phone number of that second family. I just ignored that request, because it felt so super-controlling. She says she wants the spot anyway. It was just weird, because she knows that three of my families have been with me for 2.5-3.5 years, and she knows the professions of those families. What better reference is there than that?