So, your new bunny is likely very frightened and still is settling in to her new home. This is also her third home, and she may have had some traumatic experiences in her past homes (and perhaps was even re-homed due to cage aggression). If you’ve only had her three days and are already sweeping in her cage, I think its understandable that she would be afraid. She also can likely smell a strange (and unnetuered) male near her, and it’s triggering her to protect her territory. Brooms especially can be very upsetting to some rabbits because they don’t really understand what they are.
One of my bunnies was extremely cage aggressive when I got her (she had been at the shelter for three years). When I brought her home (originally as a foster but then we of course fell in love with her), we first let her stay in her pen completely unbothered for about a week. I didn’t worry about cleaning her pen, and would very gently and slowly remove the litterbox to clean it (and slightly less frequently than normal). After that we started opening her pen to let her explore on her own. Once she was confident in coming out of her pen, I would only clean her pen while she was not in it. After a couple weeks of this, she started acting like a different rabbit. She stopped lunging and boxing at hands if I had to reach into her pen for something. I still do not do deep pen cleaning while she is in the pen though (or if I must, I always make sure she has an escape route to get out). I also only pick her up if absolutely necessary (for nail trims and deep grooming), because she hates being picked up.
At this time with your bun, I would not worry about cage switching. She needs time to settle in and feel safe in this new home. Plus your boy isn’t neutered yet so he smells really different.
So yeah, many bunnies do not like their “stuff” being messed with in their cages, so just waiting till she is out exploring to clean her cage will probably help a lot. Remember that aggression in rabbits (and all animals really) is fear-based, so providing a space that feels safe for her should help a lot.
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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.