Maybe not take him to the stores, do the shopping when Dad is there to babysit him,also stop him using the cart 3 year old's are bound to bash into folks, so no cart pushing.If he is hearing you yelling he is copying you, and you sound like you are getting into a power issue , when he is bad in the house take him quietly into time out no fighting, it wont really get his attention it will fire him up and make it worse .Is he at pre- school or daycare ,what is he like ,is he angry when he's there.
You need him to understand what a "consequence" is, and to have the consequences be something he really does not like. Once he understands what one is, you can tell him that if he continues to behave the way he is (when he's screaming or yelling) he will have a consequence. My son knows he can be issued a consequence, and doesn't like them, and he also knows he can earn his way out of a consequence (if one is hanging over his head) by doing something we name (some piece of desired behavior). At 3, your child is old enough to understand all this. Our consequences are something like -- you won't get to carve the pumpkin this evening, there will be no dessert, you have to spend some time alone in your room, we won't buy you a little toy at the checkstand next time we are at the store, etc. etc. They are not big things, but they ARE things that matter to him. You kind of have to watch carefully to develop a list of the things that he really likes, as they are the only things that work as consequences.