I have a bouncy seat, and a boppy if you need to borrow it, let me know.
As far as flying, try to make sure you feed the older one before getting on the plane and bring a backpack with coloring books, reading books, and a favorite toy that she can carry. Make sure sippy cups are easily accessible and it might be a good idea if you brought a cup with a lid for yourself since things can get clumsy while dealing with 2 children and the last thing you need is a drink spilled in your lap. I also suggest feeding the two month old during take off, that way their ears don't bother them during take off. I tried to feed my daughter right during that time. She usually would sleep through the flight then.
If you are flying out of Seattle, the flight is about 3-4 hours with boarding, in air, and landing. So make sure you bring enough things to keep your daughters attention the entire time. Hopefully, she will sleep through part of it.
For the youngest I highly suggest getting some kind of carrier like a sling or front carrier to free up your hands while on the plane, especially with a 2yo.
Also, make sure diapers are changed before boarding and make sure to put diaper cream on too, you may not be able to change any diapers until after you land and it's not fun for the little one if they develop a rash during the flight. It is very difficult to change a diaper on a cramped airplane. I speak from experience.
BTW - Where in Washington are you from? That's where I moved from.
Welcome to AZ!