Our children use both iPhones and Motorola phones. We get worn down by the fights about "confiscating" the phones, and want to be able to block access to the Internet on a device-by-device basis when we need to. Is there a router or other device/configuration that can control access on such a basis?
In your router you should be able to view all the assigned IP addresses, including their MAC addresses in the DHCP configuration. Then you could enable MAC address white-listing by entering the MAC address of the devices to which you want to allow internet access.
As you have not mentioned what type of router you have, I've added this (random) picture so you get an idea of what you're looking for:
Aside from the technical aspect, why not tell your kids they will lose their phone for a week if or when they start fighting?! And if they do it again, they'll lose it for a month.
Technology should not be a solution for your children's misbehaviour IMHO.