|"I won't have anything to do with
"I won't have anything to do with that." : Use this when you do not want to be involved with something / are disgusted by something and want to avoid it. For example, someone invites you to go rob a bank but you don't want to, so you can say "I won't have anything to do with that! I don't want to be arrested!"
"I won't have it any other way." : Use this when you want something to be done exactly as you say with no variations, especially when it's a more complex process, like a negotiation. For example, you are building a house and you want it to have four floors but your team only built three. You would say, "Add a fourth floor to this house! I won't have it any other way."
Hope this helps!