Can I control my childs phone while she is driving

This is interesting. I enabled 'Do Not Disturb While Driving' on my teenagers phones. Then I went into restrictions and enabled 'do not allow changes'. When my kids are in the car (driving or not), the DNDWD comes on, then they click the 'home' button and chose "I'm Not Driving". Why doesn't the parental restrictions disable this 100%? It defeats the purpose if teenagers can bypass it.

Disable completely no.

If its running iOS 11, you can turn on Do Not Disturb While Driving, and it will silence all calls and messages while driving. The phone can be accessed by selecting "I'm not Driving" however. You can keep this setting on, and not allow it to be turned off, by going into Settings->General->Restrictions->Do Not Disturb while Driving, and setting it to not Allow Changes. Restrictions requires a password be set, and as long as you don't give her this password, she can{t turn off the settings.

Beyond that, there is no way to totally disable the iPhone when driving.

More info here:

Use parental controls on your iPhone, iPad, and iPod touch - Apple Support

Because it is not designed to completely lock someone out of the iPhone.

The restriction prevents you from disabling the "DND while driving" option in settings. It does not mean you cannot access the phone ever once this is on.

When driving it will still offer the choice to access the iPhone, in case you need to, otherwise it may end up being inaccessible in an emergency if DND has not stopped sensing movement or continues to be connected to the Bluetooth in the car. There would be no way to access the phone in an emergency if this was completely locked down.

while you can not remotely control this directly from iOS you can look into this option.

How to use the Do Not Disturb while driving feature - Apple Support

this is why self driving cars are not a terrible idea.