My strong-willed dd would argue the hind leg off a donkey if I let her. But you have to walk away and not let that happen. You will only engage if your dd expresses herself respectfully.
What she really wanted though, and why she was defiant in the first place, was that she wanted more autonomy and choice in decision-making and independence that it would be appropriate for a child of seven, or ten or 12 to have. They are usually bright these dc. Frustration drives the boundary-pushing. So what you have to do is keep giving them activities that are just slightly above their competence level and give them responsibility and choices but within the confines of home, a sport or activity. And choose your battles carefully.
You have to have a strong boundary and clamp down on anything life threatening, but other than that, it’s often not necessary to make them compliant for compliance’s sake.
Talk through the issues with them. Is that a good idea? If so why? Give them the power to make the decision once they are aware of the pros and cons. Say things like “I trust you to make an intelligent decision”. Let them suffer the consequences though when it goes wrong and don’t rescue them from that.
And most important of all, it’s very easy to take their non-compliance very personally and feel that they are doing it deliberately to cause you grief. And yes there may be an element of seeking power and one upmanship by winding you up, but usually their outside behaviour is a reflection of what’s going on internally. So step back slightly, pause, breathe, tell her you will get back to her if you have to, rather than make instant responses, slow it all down and be very objective in how you respond. Don’t stoke the fire by allowing yourself to feel hurt. Try and look at this dispassionately as a normal albeit demanding parenting phase that will improve with time. And get up every day wiping the slate clean and expecting positive things from them. Regular one on one interaction will help.