Lots of things are at play here, and none of us can fully understand your relationship with your daughter - but a few things to keep in mind.
1. She's a 9 year old girl. Kids rebel against their parents for all kinds of reasons, and sometimes it's just a part of growing up and learning how to be independent. It's simply part of being a parent.
2. Being a child of separated parents, there's probably always going to be an attention issue. She may never understand why you separated and you may never be able to explain it to her in a way that she will accept. The best you can do is be a good mom. Most of the things you describe are attention seeking behavior.
3. It takes 2 to have an argument. Kids can certainly start or "pick" fights...but they can only continue if we engage them. Sometimes just letting things cool off for a bit is a good idea.