All children push the boundaries, that's part of their natural development, and you as a parent need to set and enforce those boundaries.
What your little girl is getting now is mixed messsages, which are provided to assauge your guilt, not to ensure she knows who is who around trhe house.
All she has learned thus far is that she can manipulate you, and she will, and it will only get worse.
So, you need to establish some rules.
Sit her down calmly and tell her she has to obey some rules, just like she does at school (and she will believe me!)
Describe your sanctions - naughty step, toys removed for a day, staying in room etc., and STICK TO THEM!
Of course she will cry - that is her button to press to get her own way, but no child ever died of crying.
She MUST learn that you mean what you say, and that punishments will be enforced, otherwise she will never learn appropriate social interaction.
Once she knows that you will not budge, she won;t push it as far. It will take a few goes, but the message will go on eventually, and she will stop before the punishment comes in - because she knows beyond doubt that it will.
You have to be tough and not give in, because to give in is not loving her, it just feels like it is, but it's a false feeling, and you will both regret it further down the line.
Children need and respond to boundaries, it makes them feel secure. Put the lines in place, ensure she doesn;t cross them, and you will both be happier with each other.
I have three daughters, all grown up now, and I do know how hard it is, but it has to be done.
Toughen up!