Its not about the 16 kids, its about the traffic from drops off and picks ups clogging up the streets during busy times. Unloading and loading a kid takes time.
There are plenty of annoyances that come with living near other people. Putting up with a reasonable level of annoyance is an important part of having a civil society. I put up with my neighbor's bullshit and they put up with mine.
And one reason people choose daycares is because they are close. Where I live anyway many of us walk our kids to daycare.
My guess is they either don't like the woman or the idea of daycare. The car excuse is extremely flimsy.
Nobody likes cars driving through their neighborhood. If these were good faith concerns, then these folks would be agitating for traffic calming measures instead of trying to quash the exact kind of business that belongs in a "residential area."