That sucks. A LOT. Gah. Sorry this has been such a hellish day for you!! I'll warn you off that bat that I'm not a parent, but I have worked extensively with this age group for quite a few years (and I still currently do) and I've encountered this problem a lot. Sometimes it feels like EVERYTHING is a struggle with this age group. If you only want a parent's perspective I totally understand, but if you want to keep reading here's my two cents below:
I've found that bribes and bargaining are a really bad way to get results. They're tempting and sometimes you feel like it's all you have to use as leverage, but they almost never work. Unfortunately if you offer a young child a reward when they behave badly (if you stop acting badly ie. do what you should be doing anyway, I will give you ice cream) it really only perpetuates the bad behavior and shows them that acting out is an effective way of getting what they want. It also shows the child that they can control you and the situation around them with bad behavior; that anger, bad language, lack of respect and other negative qualities and behaviors are effective ways to be gain power and control over others. This is NOT a good message to send, in my humble opinion!
If the kids I work with are behaving badly, I get down on the ground and request they to look me in the eyes and ask them why they are behaving this way. Kids often resist this because they feel embarrassed or uncomfortable, but that's kind of the idea. It's important to hold them accountable; when you do sometimes they immediately become bashful because they know their behavior is unacceptable. I then say something like "I know you are very smart and very considerate, so I am confused why you are making choices that hurt me and your classmates. You aren't showing me or your friends what a smart and considerate person you are. Is there a better choice that you can make right now? It makes me sad that you aren't showing me how great you really are."
I also explain (if possible) how their actions are effective others directly in a negative way. Making kids feel powerless only upsets them, and I never want a kid to feel like they have no power. They do! I like to show them that their words and actions are powerful, and have consequences, and that is the reason I am upset. Because the consequences in this case are negative.
In my personal experience I've never found that being a tyrant or a pushover is helpful - gotta meet the little buggers somewhere in the middle. I have always had the best luck with treating kids with respect and showing them that although I do have the final say as the adult, they have some say too. They have the power to make decisions about how they want their day to go - they can choose to eat lunch separately from their friends, or they can choose to sit with their friends. I am firm but I give the child the option to make a better choice for themselves before discipline; I empower them to make that better choice by telling them that they are intelligent and good, and that they have the right and the opportunity to show the world that through their actions. If I need to discipline a child I explain why I am doing this. "The choices you are making are hurtful. When you leave your toys out you make the room unsafe for me and your friends to walk in. If you cannot be nice to your teachers and friends you cannot (sit in the group, play outside with them, whatever.) I expect more from you than this, and you can join us when you are ready to act as nicely and considerately as I know you can."
Obviously, depending on the age, you have to simplify the language to make it something they can understand. Sometimes (if it's a two year, for example) I just say "Your behavior is hurting me. How would you feel if I was hurting you?"
And so on like that.
I don't know if any of this helps, it's just what has worked for me in my experiences. I recognize that it's different as a parent, although at some of the places I've worked at I actually spent more time with the kids than their parents (sadly enough.) I hope you find a solution that works for your family, and also that you don't go crazy in the process!!! Best of luck.