I think you need to get a routine established. Does she come down to the food bowl straight away when you slot it in? Breakfast and dinner? Then let her out an hour or so before breakfast (when she is hungriest) so that hopefully she will fly back in when she sees you put the food bowls in. That's how I worked it with Ollie who wasn't tame when I got him. Then I gradually increased the time he was out. It worked so well and quickly that I could let him out before I went to work.
It also sounds like you need to make going back in, and being inside the cage more reinforcing. If you give her a favourite treat to reinforce going in EVERY time then it will be more likely that she goes in, in the future. Is there lots to do in the cage? Favourite toys? Foraging? Right now it is more reinforcing to be outside the cage - how can you make being inside a higher value?
You could also break the behaviour down into small manageable steps (you'll need time for this). Reinforce her sitting on your hand whilst you move a step or two towards the cage. Then move away again. Try again getting slightly closer to the cage, reinforce, and bring her away again. This might take days to achieve... just a few seconds training here and a minute there, but worth trying because eventually you will be able to put her calmly inside. When you do reach the cage, reinforce highly!!
If you put her in, leave the door open to show her that the door need not always shut after her and she can come out again. When you do shut the door, pair it with something good like a treat.... and stay around talking to her ie. don't just leave. For breakfast when my crew go back into their cages, I have my breakfast with them. If I were to immediately leave, they would be unlikely to want to go into their cages in the future.
Just a few ideas.