Oh dear dear. One day your daughter will be a teenager, she’ll be going out on her own, and with friends exploring life, and that will be the time when rules will keep her safe. If you allow her to continue on this path by ruling the roost you are setting yourselves up for some very serious problems and worry.
It takes 21 days to break a habit, reward the behaviour you do want and ignore the behaviour you don’t want, stick it out, stop backing down and deal with the screaming tantrums by closing down all communication with her, no shouting, no speaking, no eye contact, NOTHING, because getting the tiniest bit of attention will feed her behaviour. Let her scream. When she stops tell her she’s good and that you love her, when she starts again (and she will) repeat the above, no matter how many hours it goes on for. You are the adults, but right now DD is in charge… who are the parents here? You have a duty to your DD to raise her to have good manners and to follow rules, and to respect you as her parents.
When she’s at school there’s rules, when she older and at work there’ll be rules, she’ll be told what she can and cannot do, that’s life. By constantly giving in you’re giving her the wrong message, she wins every time, she’s in charge for God sake and she’s only 6! This won’t help her as an adult because it will be ingrained that by going into a strop she will get what she wants. It will affect future relationships and friendships and that’s not fair on her.
Start on an evening when there’s no school the following day… oh and having her friend around on Saturday… tell her quite clearly when she gets home from school on Friday that if any of the screaming begins then it’s not happening, but if she’s good (no screaming) then she can have the friend over, that’s the reward for good behaviour. She will test you, she will scream, but this is where you begin, and stick to it.
The choice is yours, a few days of exhausting hell, or a lifetime of it, and eventually a ruined relationship with your daughter. She’ll hate you for a while, and that will hurt, but she needs to understand the meaning of respect, and that she cannot always have what she wants on demand, and you’ll reap the rewards of a better future with her.