My daughter is now 7 and you've described her behavior exactly, beginning at about that age. Thing is, she's a little better now. What changed? Well, at first I would feel really badly that she would say I don't love her or that she wanted to leave... Guess what?! That's exactly what they want you to feel - bad - so that the focus goes off of them and their punishment/behavior and changes to our trying to reinforce our love for them. I figured out this is basic manipulation when my friend pointed it out to me. My daughter is very smart but never underestimate the ability of a child. They can and do manipulate even from a very early age. What worked for our family is very similar to what others have written here. When my daughter is in trouble I remind her that it is HER behavior that is bringing consequences and it has nothing to do with whether I love her or not. I tell her I love her and put her in time out and we talk afterward. I warn you, it got worse before it got better (slamming dooors, banging on door when in time out, yelling from behind closed doors - all this from my precious girl who you would never expect it from). We now have an agreement that when timeout comes (they are fewer and further between now) we will not talk until 1) she has served her time and 2) she is calm (if we try to talk before this, it only starts all over). When we talk, I make sure to sit with her, talk calmly, and explain why she went to time out. If she says it's not fair, I ask her if her behavior was fair? What would she think if she saw another little boy or girl talking to her parents that way or exhibiting the behavior she had herself? This seems to be a way for her to understand by visualizing another child doing what she did. I ask her why she yelled and said I don't love her and she says she was mad that I put her in time out. when I explain that I didn't put her in time out but rather she did by exhibiting the behavior that caused her time out, she understands. Every time she ends up apologizing and ALWAYS ends with I'm sorry mommy, I do know you love me. It was the first time she said this to me, after my friend had explained her thoughts on the manipulation that I knew I was on the right track and it truly was manipulation!!!! Understand that your child is only trying to feel their way to how far they can get and what will and won't work. I was so taken aback by my daughter who I love with all my heart saying "You don't love me" that I began to focus on how could she think that and try to make it better. When my friend pointed out her observations and as soon as I stopped explaining myself and stepped away by initiating the time out method I spoke of above, the situation has pretty much petered out. Good luck. Know it's not you. Your child is just growing up... Best Wishes!!!
PS. Now the manipulation is mom i just want to talk about it. My rule is we don't talk about it until after time out (because she gets too heated)... but mom I just want to talk to you (tears!)... It's another method of delay and manipulation. I tell her that we will only talk after her time out is over and after she is calm and we do... Just wanted to add the PS so you know it's not over just because it's over... there are other methods... Just hang in there. You'll both get through it. My daughter and I have the best relationship and are very, very close so don't stress, it'll all work itself out. It's just part of them trying to grow up. The way I look at it is I'm getting the manipulation lesson now in the early years rather than being sucked in and manipulated in the teen years (though I have no doubt it will continue even then LOL but at least I have experience.) :-)