First, I'm glad that no one was hurt. Especially the kids.
And sorry about the accident.
There should be an 800# on the lease paperwork/statements. But your insurance agent should be able to help you with this: if the guy is proven as DUI...he has zero defense and has to pay.
If he's an uninsured motorist, you should have that spelled out on your policy, what you're covered for under those terms.
But your agent has all of this at the tip of the tongue, so I'd call him/her tonight, just to get the ball rolling. Claims are handled in the order received: call tonight.
At first I thought you meant a rental car, which is an entirely different can of worms. (always always rent with a credit card: currently VISA pays out the most for this kind of crap)
Good luck!