You could send the child ahead on another flight with your spouse or maybe a grandparent, or consider leaving her home locked in a closet. Since neither of those are going to work, I suggest a few things. First, book the child a seat.Her own seat. The lap thing is not going to work. Pack a carry on,(she is entitled to one too) with all kinds of diversions. Whatever she likes, crayons , stickers, books, stuffed animals etc. Have plenty of diversionary materials. Pack snacks , juice boxes , milk etc. whatever you allow her to eat and drink. Make it a variety. Consider purchasing a portable DVD player (with head phones) . Two movies and the flight is over. If not that, a portable tape or cd player with Sesame Street Music, nursery rhymes, Kids Bop, stories on tape etc. New books to read or old favorates. A small blanket, it can get cold on a plane.
No bottle or gum to chew to ease ear pain? Put water or juice in a sippy cup(even if she has outgrown them) . Works just like a bottle for clearing the ear pressure. Make it a game.
I also suggest tranquillizers. Not for the child, but for you, your spouse and the 12 closest passengers. (just kidding, or maybe I'm not)
I Think she will surprise you . The "adventure" of being on the plane will occupy her as well.
One last thought. When she pulls at your sleeves saying Mommy or Daddy, answer her the first time and every time. Having sat near children on hundreds of flights the usual difference between "good " kids and "bad" kids was in the attention they got from their parents.Nothing is worse than sitting near a kid saying Mommy a 100 times while Mommy is plugged into earphones and watching a movie.
Have a wonderful time. Two year olds are a joy.