I have experience with only one child, now just graduating from High School, but if memory serves, YOU WILL NOT SUCCEED IN KEEPING HER IN HER SEAT FOR FOUR HOURS, unless you are travelling overnight.
Take her for a walk, play hard with her in the gate area, before boarding. Feed generously just after taking your seat, and hand out favorite snacks whenever she begins to fidget.
If possible (only mom knows), wake her up a little early, keep her active just until you board...maybe she will take a little nap. I've often thought that noise is the hardest thing forthe little ones to handle, as the noise level is really different from their experience, and is what disconcerts them the most. It is also what makes the kids so loud - they are hardwired to make 20db above the noise floor, so they can be heard! With the advent of the cheaper, noise cancelling headphones that happened after my daughter was older, it might be a good thing to try to prevent noise fatigue (and damage) by providing one of the $49 Aiwa or equivalent headphones - they really help me and my family travel, and they fold up pretty small - we found ours at Best Buy. They come with adaptors for the airline jacks.
If she likes to color, take a fresh coloring book, and a small assortment of crayons, but try to account for them all when you debark, as it is a disaster for others' fine suits and dresses to have a melted blob of some non-matching color upon arrival.
Keep a sense of humor, as all humans must pass through this stage, and if others are not a little forgiving, then they must not be human. Don't let some sheisskopf make your trip anything less than a glorious adventure - parenthood/kidhood is a blessing, not a curse. You and your child deserve to be there NO LESS than anyone else, and everyone on the flight has some small imperfection with which we collectively must be forgiving, like being overwide, over-perfumed, overbearing, too old, too young, too tall, etc.
Love your little one, be patient, and defend her against other's complaints.
Best wishes, and good luck.