In answer to the question "where is his time-out?"
Our time-out spot is a little hallway ending, nook type spot between the bathroom, bedroom and kitchen. We put up the baby gate, and the child is in a square space about 2.5 feet square. Nothing else is in there. The walls are white. Nothing to see, nothing to do. We walk away and he/she is all alone. Both kids are capable of simply moving the baby gate, but they don't. They know that this is time-out, and you stay until Mummy says so.
We may have found something that works. Last night we took away a toy he was misbehaving with, and he really didn't like that. So I'm thinking it's time to take things away. He hates to lose his "baby". This little plastic dolly sleeps with him, and he carries it around quite often in the house. Perhaps losing "baby" when he does something like hitting will make him think twice.
Truly, he's a wonderful little boy. But he's two, almost three, and it's time to push Mummy and see what happens!