First of all, if you are fat, you need to not be ashamed of it. Teach your kids, explicitly, or implicitly that while you are overweight, it's not a character flaw. It's a physical feature that is no more shameful than height, eye colour, freckles. the reason I say this is because children are parasites and they will exploit any weakness you show them to get more out of you. If they know you don't give a shit, it won't work as an insult.
There are very, very few times that my children have upset me personally. When they have done this, I have been very clear: I'm actually upset by what you said to me. I do not wish to be friendly with you. I will continue to feed and take you where you need to go and exchange information, but do not attempt to converse with me until tomorrow. Children are herd animals and hate to be excluded. This works for me, but won't work for everyone.
The hitting needs to be punished, especially if the child is in full control and not overwhelmed/having a meltdown. Do not hit back: You lose the moral high ground and don't solve the problem.
Your kids need to earn these treats, as they feel they are being robbed of what they consider to be an entitlement.
Their dad needs to be on board with the expectations and sanctions. I hope he/you do not insult each other.
If they have ipads/phones, or know how to use such devices, this stops immediately. I should have put this first, as this is often the cause and removal is solution.