Can you get an exception on early withdrawal from IRA for taking permanent guardianship of someone's children?

Guardianship, no.

You can claim an exception to the penalty for up to $5000 for birth of a child or legal adoption.  The withdrawal must occur within 1 year after the date of birth or date the adoption is finalized; withdrawals before the date are not eligible for the exception.  

You can claim an exception to the penalty for up to $1000 for any emergency personal expense.  "Emergency personal expense distribution” means any distribution made from an applicable eligible retirement plan to an individual for purposes of meeting unforeseeable or immediate financial needs relating to necessary personal or family emergency expenses."

There are some special rules for the emergency expense withdrawal.

1. You have 3 years to pay it back if you want to.

2. You can't claim the exception again for 3 years unless you either,

a. repaid the previous emergency withdrawal, or 

b. have made new contributions to the IRA that are at least as much as the previous emergency expense withdrawal. 

3. Even if you repay a previous emergency withdrawal, you can only claim the exception once per year.