SBG10 model doesn't have any settings like manage devices on the modem GUI. could you please help us with the brief explanation on what you are trying to do on the modem GUI exactly.

I would like to pause the internet on my child’s devices at bedtime so that she isn’t up too late. 

Yes to pause or to block any specific internet websites from your child's device in SBG10,  follow up the below link on the same:

http://arris.force.com/consumers/articles/General_FAQs/SBG10-Parental-Controls-Setup

Thank you. I am having trouble logging in. I get an error message saying that the username and password are incorrect or my account is locked due to too many incorrect attempts. 
 

what can I do?  I don’t recall ever changing the password. 

If you are not sure about the password to login the GUI web portal, I suggest you to factory reset the modem and login with default password as password.

To perform factory reset, let me send you the link for your reference:

http://arris.force.com/consumers/articles/General_FAQs/SBG10-Factory-Reset

Hope you were able to log in on the GUI page after the factory reset. 

After logging in to the GUI Were you able to pause or block any specific internet websites from your child's device in SBG10the parental control?