Bringing your squirrel outside to run around free, is in essence a soft release. I doing this you are sending her contradictory signals as to expect her to continue to act like a pet, yet supporting her independence from you.
You need to make a decision to keep her inside supporting her with an indoor surrogate arboreal habitat, or to release her.
If you want her to remain your pet, she needs to be taught to be submissive. This though isn't a matter of being aggressive as to enforce submission, but rather to gain trust through gentle domination, not allowing her to hoard nuts in her cage.
One thing that can really help we found to work well for an aggressive female is to respect her eating space.
For our aggressive female, after she attacked my husband at 2 1/2 years of age, biting him repeatedly when he reached in to give her his usual kiss good night, instead of seeking to dominate her through force, having removed her cache of nuts (which our fault for allowing her to cache them, setting her up to be protective of her cache), I went into her large cage and kneeled down within about 2 ft of her on her nest platform, keeping my hands out of sight, gave her good talking to using a low slow serious but not angry voice. To this she responded by backing up and making a whimper to show her submission to me. I responded by keeping eye contact with her, all the while continuing to speak to her kindly, Id slowly reached wide behind her with my left hand cupped to gently pick her up and pet her to let her know I approved of her response. I never had to do that again. As for my hubby, I advised him not to reach for her in her nest, but to let her come to him. In doing this he found she came to him willingly, never again showing him the aggression as she had prior.
As for using a harness and leash, for a more dominant squirrel this may not be accepted if not trained prior to reaching adulthood at a year. With our oldest squirrel it took a period of time to condition her to the harness, putting on it for 30 sec. to begin with then a bit longer, tow here she didn't mind wearing it. Thing is the leash was an issue and since she could get out of the harness I gave up on using it.
Instead of outside activity, bring some of the outdoors indoors by creating a large habitat cage with safe woods for platforms and branches that are well secured so they won't move when climbed or jumped upon by the squirrel.. Here is an example of such a cage. I don't recommend though it be built outside, save on an enclosed patio.
https://www.youtube.com/watch?v=Ys874rv-wXM
I hope this helps.