I'll be the sourpuss: I'm against the midwife bringing her kids to your birth.
First off, let's be honest: school-age children are, universally, filthy little disease vectors, and you should at least get a few feedings in before exposing your newborn to them.
Second, if there is an emergency regarding the visiting child, the midwife will not be able to focus on her job. I don't care how professional she is, that's just human nature. So find a midwife who is willing to eliminate the distraction by obtaining child care for herself.
Basically, I view "Can I bring my kid to your birth" as a warning sign. What it's warning you about is that the midwife's professionalism is suspect.
Maybe everything will go great with the midwife's kid there. Maybe it won't. But it's another variable. Planning a successful birth is about removing variables, not adding them.
The examples people have given in this thread to justify this are "Oh, if the visiting baby is crying during a crisis, I'll just ignore it until the crisis has passed." But as a pessimistic dad, I can think of hundreds of other scenarios, some of them downright likely, that would be worrying me. Suppose you're in a labor crisis and the visiting kid falls down the stairs, or some similar physical trauma? Now you've put your client (and yourself) in a position where the responsible adult is going to probably do harm to one of two children, or if they're really unlucky, both.
Having an extraneous kid at a labor is the quintessential example of a thing that sounds awesome, after the fact, when everything went great, and sounds incredibly stupid when something went wrong. So personally my advice would be to not take the risk. And I have no problem describing "Can I bring my child with me to this life-changingly important event that you are paying me to work at?" as "unprofessional."