Hmmmm, this is very interesting, and I can see how it would be very stressful.
How frequently would you say you need to corral her by chasing, or have to pick her up?
To me this reads as though she has gotten somewhat territorial, and that she anticipates negative things happening when you approach. It’s also very odd that she won’t take a treat from you.
Can you post a picture of her? (If you add the pic to her profile you should then be able to add it to the post from your media library… we are still working out some glitches).
Here’s what I think I would try…. I would stop the backyard sessions for now, roaming in the room is plenty of exercise. I would also attach an x-pen to her cage, and have that be her home base that she has 24/7 access to. Then, I would only allow free-roam of the room while you are there, for several hours a day (so you could do a few hours morning and evening, or even overnight if you choose). The idea is that you want her to associate more space with you, and not think that you are invading her space (if she views the whole room as her territory).
You mentioned she gets apples in her food bowl, so she might be getting too many treats. I would work on hand feeding her as much of her salad as you can, and all of the treats she would normally get. If she won’t take it from you while you are sitting in the pen, try sitting on the other side of the pen and feeding through the fence bars. You can use her pellet ration to get her back into her pen when you need her to. Aim to use something positive to move her around when possible, rather than shooing her. I’m basing this off the socialization program we use at the rescue I volunteer at, btw.
Clicker training can be a really great tool for bonding with bunnies, and could help you with other necessary things (moving her around, nail trims, etc.). The fact that she comes up to your feet and nudges is a good thing. My bunnies do this too, but it’s not aggressive. Sometimes it means you are in their way though, lol
For picking her up, you can try training her to go into her carrier, or pick her up while she’s in her litter box. If you must pick her up without doing that, try not to chase. Approaching from the side helps too. Here’s a vid of how I pick up difficult-to-handle bunnies at the shelter: https://drive.google.com/file/d/12iIW-I7CAJIK7Zah6jN0470eQkOlaqr3/view?usp=sharing
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.