Hello and welcome. Thank you for requesting me. I apologize for the delay. I was not online at the time you posted your question, and I'm not sure why I was being shown as online. I'm sorry to hear you are having this problem with Sunny. She/he is quite pretty.
Every budgie has a unique personality, and you got lucky with your previous bird. You have done most things right, but some budgies just take a little more time. A budgie will bite for several different reasons, including fear, stress, being tired, and defending itself, among others. Because Sunny wants to be in the cage, I suspect there is something about being out of the cage that is stressful. If he/she bites you and you put her/him back in the cage. You are in effect giving a reward for biting. Even saying no, especially if you raise your voice or change the tone a little, can be rewarding. If you've heard budgies chattering at each other, you know how loud they get. Being louder can be seen as something good.
The best thing to do is ignore bad behavior. That's hard when you've just been bitter, but if you don't react in any way, there's no chance of rewarding what you don't want to. Instead, reward when there is good behavior. If the bird sits quietly on your finger, even for a few seconds, give a favorite treat.
Since being out of the cage must bother Sunny in some way, I would also suggest that you start all over as if you just brought the bird home. No flying around the house, etc. For the first week of this program, it would be a good idea to keep the cage partially covered to make Sunny feel more secure. Put the cage in a room where you spend a lot of time. That will help her/him get used to your presence and to help to realize that when you move about, there's no danger. Talk softly from outside the cage, but don't try to put your hand in just yet (except for routine care). After about two weeks of becoming accustomed to family activities and listening to you talk from outside the cage, you can offer her a treat, or just let your hand rest quietly in the cage. When Sunny is at ease with that ( no biting), you can go back to finger taming. Work only on that for about a month before trying out of cage time. There are no shortcuts to taming - you'll need patience and will simply have to spend time at each stage before moving on.
Taming a difficult budgie requires a lot of time and patience. Once in awhile, there is one that just won't respond, but that is unusual. I hope Sunny will respond well to starting over and ignoring the bad behavior.