oh mama, buy the tickets for the flights for her and just bring the carseat onboard. you will all be so much more comfortable. it sounds like the united flight (is it? we took that one recently), and if you call them up, you might be able to get a discounted ticket since she will still be considered an infant (under 2 years old).
ask if the bulkhead seats are available so you don't have to worry about her kicking the seat in front of you. you'll have to stow your carry ons above, but for us it was less worry than constantly having to feel bad for the person in front of him and apologizing about his little pushes. NOTE ABOUT BULKHEAD SEATS: the armrests do not flip up between them because the tray is stowed there, so if you are a bigger person (i wear a size 12 and it was a snug fit for me; my partner has a 36" waist and a slightly bigger belly and it was definitely snug for him) it may not be as comfortable for you.
if you really, really, really can't swing the ticket for her, reserve the window and aisle seats so it is less likely that someone will want the middle seat. and if someone does end up sitting there, they will probably be very happy to switch seats with one of you. and when you are checking your luggage and checking in for the flight, ask the agent if there are any available seats for you to bring the carseat aboard and use. even if they say the flight is full or pretty full, ask if you can check with the gate agents just before the flight and then gate check the carseat if there are none. also ask for a big plastic bag from the check-in agent as they generally don't have them at the gate.
i would recommend bringing the stroller as you can always gate check it, and your daughter may want to ride in it or if not, you can stow all your stuff in it and only have to worry about carrying her and pushing the stroller. if it's really big monster stroller, definitely look into buying or borrowing someone's lightweight umbrella or traveling stroller (we have an awesome lightweight little-bit-more-than-an-umbrella-but-not-a-full-on-fancy stroller called the Combi Savvy we got at a secondhand store)
definitely bring the sling, or better yet, a two shoulder carrier like a wrap or an Ergo or a mei tai. and be prepared to have to take her out of any carrier when going through security. when we traveled about a month ago with our then almost 21 month old son (who is small, by the way, at 23 lbs and about 31", but we still bought a ticket for him) i carried him on my front in the Ergo, put his diaper bag backpack on my back and carried a tote bag for snacks, toys, an extra sweater for myself over my shoulder, while daddy carried his backpack and handled moving the carseat onto and off of the plane and closing up or opening up the stroller at the end of the jetway. then we loaded all my bags onto the stroller and walked through the terminal.
hope that helps! feel free to ask me any questions i didn't address!
~claudia
ask if the bulkhead seats are available so you don't have to worry about her kicking the seat in front of you. you'll have to stow your carry ons above, but for us it was less worry than constantly having to feel bad for the person in front of him and apologizing about his little pushes. NOTE ABOUT BULKHEAD SEATS: the armrests do not flip up between them because the tray is stowed there, so if you are a bigger person (i wear a size 12 and it was a snug fit for me; my partner has a 36" waist and a slightly bigger belly and it was definitely snug for him) it may not be as comfortable for you.
if you really, really, really can't swing the ticket for her, reserve the window and aisle seats so it is less likely that someone will want the middle seat. and if someone does end up sitting there, they will probably be very happy to switch seats with one of you. and when you are checking your luggage and checking in for the flight, ask the agent if there are any available seats for you to bring the carseat aboard and use. even if they say the flight is full or pretty full, ask if you can check with the gate agents just before the flight and then gate check the carseat if there are none. also ask for a big plastic bag from the check-in agent as they generally don't have them at the gate.
i would recommend bringing the stroller as you can always gate check it, and your daughter may want to ride in it or if not, you can stow all your stuff in it and only have to worry about carrying her and pushing the stroller. if it's really big monster stroller, definitely look into buying or borrowing someone's lightweight umbrella or traveling stroller (we have an awesome lightweight little-bit-more-than-an-umbrella-but-not-a-full-on-fancy stroller called the Combi Savvy we got at a secondhand store)
definitely bring the sling, or better yet, a two shoulder carrier like a wrap or an Ergo or a mei tai. and be prepared to have to take her out of any carrier when going through security. when we traveled about a month ago with our then almost 21 month old son (who is small, by the way, at 23 lbs and about 31", but we still bought a ticket for him) i carried him on my front in the Ergo, put his diaper bag backpack on my back and carried a tote bag for snacks, toys, an extra sweater for myself over my shoulder, while daddy carried his backpack and handled moving the carseat onto and off of the plane and closing up or opening up the stroller at the end of the jetway. then we loaded all my bags onto the stroller and walked through the terminal.
hope that helps! feel free to ask me any questions i didn't address!
~claudia