How can I keep my cat inside?

My cat is a little under a year old. She's spayed but not declawed. I wouldn't have a problem with her being outside except for the fact that we live on a busy road and our neighbors have aggressive German Shepherds... Anyway. We have an automatic dog door for our two dogs that open automatically when they go near it because of sensors on their collars. Well, my cat has figured out that she can go out when the dogs go out. She usually goes out at night time and comes back around 3 in the morning. The problem with that is that everyone is asleep, so no one can let her in. I'm very worried about her. She's already gotten stuck in the neighbor's tree once and it took forever and a fireman to get her down. We've tried spraying her with water when she gets close to the door, but that doesn't work either. Does anyone have any suggestions? Thanks ahead of time.