I am not against spanking, or spanking with a belt (but I don't use a belt). I know what you mean about wanting respect from your son; they can be really defiant and it gets frustrating.
I went through this same phase with my son a few months ago, and I decided to put an end to the defiance and the hitting, spitting, backtalk, kicking, pinching, and punching by taking an absolute zero tolerance stance (and he learned the hitting, etc. from the kids at his daycare and from seeing stuff on tv, even commercials).
If he so much as raised his arm to hit me, I'd catch it and put him in time out in a corner in a dark bathroom (with the hall light on). He had to stay there for three minutes for each offense, not for each year of his life. So, if he hit me, then spit while I took him to time out, he'd get a six minute time out.
If he ignored me for something like, "come here please," I wouldn't even bother to say it a second time. He'd go to time out if he did not respond the first time.
For a week, we went through this, and it was the longest week I've ever faced with him. But I only resorted to spanking him twice. I decided I'd nip the disciplinary issues in the bud before getting frustrated and angry with him.
And if he refused to stay in time out, I'd stand outside the bathroom door where he couldn't see me, and if he tried to come out, I'd put him right back. I'd do this and restart his time each time he'd attempt to come out. I only had to put him back in time out for about two days before he decided it was easier to just stay there and serve his time.
He's much better behaved now and almost never hits, etc. He still has issues with backtalk and subtle defiance (like if I say, "don't come in the kitchen right now," and he puts his toes onto the lenolium floor and gives me that mischievious grin like, "I'm not completely in the kitchen, so what are you gonna do?").
You have to take your stand by setting firm bounderies and sticking to them. Sticking to them is the hardest part, but you can keep from getting frustrated and angry by stopping things before they get started.
One thing I am also wondering, why is he apologising to you for hitting his mommy? Is she doing anything to help raise this boy, or does she play and play and wait for you to yell or whip him? I also worked in a daycare for quite some time and the only time we had children act like this was if they had a new teacher that was not cutting it. Judging from your own seeming anger issues, a very big good luck goes out to your son for his future.
How can you expect this small child to respect you or know that hitting is not ok when you beat him with a belt? I am the mother of three children, two of them very difficult....and I have never resorted to beatings. You have to earn respect, even from your children...you are not entitled to it just because you are their parent. There are alternative ways to discipline a young child, using a belt on a three year old should be illegal. I have a three year old, and I can not imagine his sad little face if I hit him with anything.
Just my opinion.
Adults do not deserve respect from any other human being unless they earn it. Take a good look and make sure you have earned respect from this 3 year old. Also, try to remember that he is only 3 and not 13 or 30