I am flying by myself next month with the two kids (3 years old and 9 months old). For those who have done this, what are your suggestions?

I am planning on using our double stroller, so I think getting through the airport should not be a huge deal. I will then gate check the stroller. The most difficult part will be getting from the car to the check in. I will have two kids, the stroller, two car seats, and luggage - and ONE me! The plan is to bungee cord the car seats to the double stroller and use my ring sling to carry the baby. I can then push the stroller and pull the luggage. The 3 year old will walk. Once at check-in I can then check the luggage and car seats.

Does this sound doable, or am I crazy?