There is most likely no parent that the idea has not crossed their mind

. Would I do it? Nope, but it has crossed my mind at least. I would take your baby's car seat and pray for an open seat. If not, you can gate check it. So as it sounds, you are going, no medication, and no assured seat for the baby. So lets get you as many ideas to make this flight as easy as possible.
-If your child is still on the bottle or passie, don't take him off before the trip. Both can be invaluable. Don't stop nursing either if you do that.
-Take tons of snacks. Lots of fun, snacks that take a long time to eat and have some play value too, think teddy grahams, gold fish etc. You can purchase drinks after security and you can take formula on the plane with you.( a bonus for keeping little one on it).
-If you have a choice, time the flight for when you think you have the best shot of getting them to sleep.
-Enlist the help of your 4 year old. Play up her as your helper. Be sure she can pull her own luggage.Wear your baby. Maybe the promise of a big sister reward at the end of the trip. She can be a lot of help handing you things out of the bag etc.
-Pack well but not over pack. Take all of the diapers, food, ect you could need and then double it. You never know what delays will happen.
Pack less but well thought out toys.
-ipad or iphone downloaded with tons of stuff for your 4 year old. Be sure he understands the no electronics on take off /decent, and that he must wear ear phones or use no volume. Books are good, magazines are good (and can be tossed), stickers and paper, color wonder books etc.
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dress them in as easy to handle clothes as possible. Think through changing a diaper while supervising your 4 year old, and taking your 4 year to the bathroom as well.
-Take a small blanket for each....it can be cool.
-Be well rested yourself and just accept the fact you will spend every second trying to keep them happy and quite.
GOOD LUCK