I'd bring the stroller...you don't take it on board; they let you bring it all the way to the plane and then they take it underneath...you get it back when you get off (get off the plane and wait right by where the luggage guys come up...they bring up the strollers & wheelchairs a few minutes after landing...ask a flight attendant if you don't know where to wait for the stroller. You might want to bring the bjorn too so you're hands-free to deal with your toddler getting on and off the plane and getting settled. And I would definitely want the stroller for her in the airport, so bring both. You'll be THRILLED you brought the stroller especially.
I always bring a few disposable changing pads...great to use on airport bathroom changing tables and also if you need to lay the baby down on the seat on the plane. At Target - get the 10 pack...those are the big ones.
For the plane...be sure the baby has a pacifier, bottle, or is nursing during the ascent and descent of the plane. For your older child bring some gummy candy...not the healthiest of foods I know but you can get some organic ones from Whole Foods or Trader Joe that aren't so bad. But they are excellent for helping with ears on the plane...plus they are a treat so that makes for happy toddlers! I think 2-3 is way too young for gum. Also have a drink handy for her...the chewing and swallowing is what you want her to do for the pressure in her ears.
Buy some of those scented plastic bags (Target baby section) in case your baby has a poop during the flight or heaven forbid, one of them throws up during the flight...even if they just get wet it's a great place to store their clothes so you don't have to just throw them in your bag with your clean stuff. Be sure to bring change of clothes for both kids...outfits that will fold up very small and not take up a ton of space in your bag. Bring a bag/backpack for your older daughter...she's allowed a carry-on too. That's where you can store your snacks, books, little toys. Be sure to have a brand-new toy in your bag for any in-flight toddler meltdowns. I usually bring a small portable DVD player and small selection of movies too.
Fill up your daughter's sippy cups (I do 1 water, 1 milk) before the flight. It takes forever and a day to get anything from flight attendants usually. When the flight attendant does come around, get a cup of ice for your daughter. It's amazing how long a cup of ice can entertain a child. Be sure to pack a couple of small washcloths in your bag (those thin baby ones take up hardly any room) so you can easily wipe up little wet messes without having to fumble around finding napkins.
Last suggestion - bring stickers...the worst part of any flight is once you've landed and taxied to the gate and you have to sit there for an extra 10-15 minutes before you can get off. Put them on your nose, the baby's nose, your daughter's nose, the seat in front of you, whatever...it should buy you just enough time to keep her happy until you can stand up and get off the plane.
Best of luck - I've done it many times with my 2 kids (now 2 and 4) and I always feel like I'm preparing to go into battle, haha! But if you stay calm it can actually be fun.