A few practical things while you study up with some of the books the moms have mentioned.
Make sure his hearing is clear. If you in a normal voice from behind, does he hear you? When you are in the car, with no music, can he hear you?
If not, consider having his hearing checked.
No more yelling across the house, over the TV or the car radio. ALl of you go to each other to speak with each other. The effort wil show you are serious.
When you are giving him directions, get down on his level and look in his eyes. Say his name if you need to get his attention.. Tell him.. "Listen to my words." Have him repeat the instructions to you. Thank him, when he repeats it back correctly.
Remember, the word "Behave" is an abstract word to a toddler. They need specific behavior words.
Hold my hand, Stop. No running. Look with your eyes. No touching, hands behind your back, Sit your bottom in this basket.
One instruction at a time. Tell him thank you each time he follows the direction as requested. "Thank you for sitting down!" I like how you are walking with your hands behind your back.
"Quiet voices", no yelling inside the store, the house, the car (whatever place is appropriate). Tell him this before you go inside or before you leave the car. Give him a complement when he follows this direction.. even more attention when he does it on his own!
"Soft and gentle touches."
Take a belt with you and use it to strap him into the basket, the stroller, the chair at the restaurant. Buckle it behind his back through the slots of the basket, stroller.. whatever. . Buckle it just so he can not get out of it.
This is pretty normal behaviors for a 3 year old, BUT we do need to continue to guide them and remind them of the expectations.
Remember children learn proper expected behaviors, through positive attention than punishment..
Yes, it takes, patience, it take your time and you noticing him more often, but he is worth it.