I agree with you completely that renting carseats is a bad idea, fwiw. I do have three kids, but two are babies (6mo) and I haven't flown alone with all three yet. But we do fly regularly with kids and carseats!Â
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My ideas:
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Can someone at your destination pick up a new scenera for you? It would certainly fit your youngest, and that would be one less seat to schlep.Â
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Do you own, or can you borrow, a double stroller? Even if none of the kids ride in it, you can pile stuff into it. Stack two of the carseats in one seat and one carseat in the other seats, with your carryon suitcase on top... Plus I find a stroller very helpful for my 3yo to hold onto when she needs to remember to stay with me.
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Or, if you can buy/borrow a luggage cart, you can strap one carseat to the luggage cart, put a bag in the carseat, then strap a second carseat upside down on top of the luggage (bring bungee cords). If your carryon bag is a rolling bag you can strap the third carseat to that, and pull the two rolling items with the 1yo on your back.Â
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Check out the Ride Safer Travel Vest for your bigger two kids. It would be a pricier option, but very convenient. If you fly or carpool regularly or if you could resell it after you use it, it could be worthwhile. You could pack the vests in your luggage and only deal with one carseat (for the baby). The one carseat can either be attached to your rolling carryon suitcase or on a luggage cart for easy carrying. Or if two RSTV's is too expensive you could get one for your 4yo and only deal with two carseats. The one vest could be passed down through all three of your kids on future trips.  Â
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A tip:
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Leave a LOT of extra time for security. You're going to have to disassemble whatever tower of stuff you've put together, get all the stuff through the scanners, get the baby off your back, deal with everyone's shoes, etc. Then once your kids are all freaked out by the weirdness of it, you have to try to keep them from running off while you get the shoes back on and everything reassembled.  It can be done, and likely total strangers will offer to help you, but it will be a bazillion times worse if you're in a rush. We flew a redeye with two 3mo babies (twins) and a 2.5yo (two adults, thankfully) and it wasn't awful, except for the security part.
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Are you buying a seat for the 1yo or will he be a lap child? If he's a lap child you'll have to gate check his seat (which is very easy, IME). Regardless, board as early as humanly possible so you can get yourselves situated.
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