There is also the flip side of being polite - people who want the best at the last minute.
I volunteered at the MN Science Museum for it's grand opening (new location) specifically so that I could see Bill Nye the Science Guy. I grabbed a spot in an odd location, but I could see the whole area, and have something to lean against. I claImed that spot about 20 min before he was set to begin. About 2 or 3 min before the start time, a mother started harassing me to move so that her kids (about 10 and 12, I think) could see better. If I had moved, then I wouldn't have been able to see at all!
I agree that all people should be able to see, but why should I have to defer to a child, just because they're a child?
On topic - I'd say that when you left your seat, unless someone was saving your spot for you, that woman had a right to sit down. If you leave a deck chair, how does anyone know when you'll be back? How did she know you'd be back?