For me, I find that my female Quaker can be nippy when she is going through the hormones season, if I am not paying direct attention to her, or if shes excited (I will have a dance party with my Quaker and Sennie, and inevitably, my Quaker will fly to my shoulder and give me a pinch on my face or neck if I dont have her step on my finger right away). When she is first let out of her cage, I engage her in some direct play and scritches, and since she was the first bird I adopted, I make sure she sees that she gets my attention first.
In addition, when my Quaker bites, I tell her verbally to "be nice" and will put her on her playstand for awhile, or if she is really crazy, in her cage for 5-10 minutes before letting her out again. It hasnt stopped her from biting me, but it does deter her somewhat. I also try to provide her toys and treats to occupy her if I have her out.
I agree with everyone else's advice that birds and small children need to be monitored when together. To help your Quaker and your kids to socialize, it may be helpful to just have them observe one another in the same room, and in the case of your 4 year old, to have him/her talk to the bird and offer the bird treats, like a sprig of millet, veggie piece, etc, under your supervision without petting or otherwise touching the bird. For our nieces and nephews, I explain to them that birds are scared if they move too fast and I will teach them how to put out their arm out for my bird to step up but I do not leave the bird on their arm for more than a few minutes, and then I will also provide my bird a treat for her good behavior. I will not do this, however, if I see my bird cowering to be closer to me or otherwise excited.
