If you are having trouble extorting business owners, try destroying some of their property and/or hold a gun to their face. For example, when you are trying to take over Good Eats in Brooklyn, you can hold a gun to the man's face then reholster the gun and extort. If he refuses, simply draw your gun again, lock on, and hold it. Keep doing this until he caves in. Do not forget to reholster your gun to avoid accidentally shooting him. In another example, when you are trying to extort money from the hotel owner in Brooklyn, hold a gun to him twice, break the downstairs cupboard, then finally blow his safe before you beat him into submission. Always buy available rackets first. Take a trip around to either buy another racket or go around the block. Do not attack until you visit again, and instead of enemy soldiers you will find all your soldiers. By doing this you do not have to fight a bunch of enemies and get your vendetta up.
If you have not taken over all the businesses and rackets, wait until you have reached the Don Of New York City rank. You will be able to take over anything without having to smash anything up or convince the person that it is a good idea; they will just say Yes immediately.