If it's in kids mode, then the owner of the phone will need to enter the password to access parental settings or exit the mode.
There's really no easy way around it. Its a security thing. The phone pretty much stays in the state it was locked in (meaning you can't access settings, turn radios on/off).
Imagine if you lost your phone with mobile network data turned on. A dishonest person could pick it up without knowing your password and put it in airplane mode which would prevent you from locating it.