I wouldn't bring a stranger into the house during daycare hours, and if I absolutely had to, I would notify the parents beforehand.
I woulnd't have a problem interviewing a "dad" though. I'm not sure why that is in quotations. I don't think it's fair to make assumptions just because he's a guy. A friend of mine just interviewed a single of father of 6 children, because his wife just passed away. Some fathers may be single, some fathers may be the one in charge of finding childcare. I would definitely not have a problem bringing a man to my house who is looking for childcare, provided I do an initial phone interview, like I do with everyone else.