Thanks, all. It is out of IAD, and we'll have three young kids and luggage. So, I called the airline to see what they thought. We'll do the international check-in at IAD, so it doesn't matter that the first leg is domestic. But, the ticket counter doesn't open until 3:45, so we were advised to arrive at that time.
Oy. I don't remember the thought process that went into getting these tickets. Likely cost and the appeal of having most of the day at the destination and likely no thought to the 2 hour rule. Oh well. It'll be rough, but then it will be over.