I agree, I think the way you are handling the situation is counterintuitive to your bird. She has developed a fear of being locked inside her cage all the time, so she flees every chance she gets and does everything she can to not have to go back in.
I have never used a bird's cage as a form of punishment or as a "time-out" location because it's the bird's home, it's safe-haven that it should like and want to be in at certain times. If you use it as punishment or the time-out location, your bird only becomes totally confused and will try to avoid it at all costs.
How many hours does she get out of her cage per day? Do your birds have a separate T-stand or playstand that they sit on during out of cage time?
I do not think clipping her wings is the answer at all in this particular situation, and I'm actually a fan of clipping wings when initially training a new bird. As explained by Violet_Diva you need to train your bird to do what you would like her to do when you open her cage door, as birds do not "just know" or "just realize" what they are supposed to be doing. If you train her using POSITIVE REINFORCEMENT, like showing her where to go and rewarding her with treats when she does, rather than using negative reinforcement and punishment when she just wants as far away from her cage as she can get because she now knows that she will be stuck inside it for a long period of time once she is caught, you will see positive results fairly quickly. Birds are very intelligent and they respond to positive reinforcement very well, but in my experience birds very seldom respond to any type of punishment. They are not dogs.
The other thing you need to remember is that both of your birds need at least 3-4 at a bare minimum of out of cage time each day to keep them happy, entertained, and healthy. I don't know what your situation is regarding their daily out of cage time, but if they are not getting 3-4 hours per day at a minimum then this also has had an impact on her behavior. If you couple a regular, daily, sufficient and quality out of cage schedule and combine it with training and positive reinforcement, and you remove all negative reinforcement and punishment, you will get the results you are looking for and more importantly you'll have a happier bird.
"Dance like nobody's watching..."