Hi R.. You've received some great advice. I have to say I truly agree with Kathy A on many of her points. I know this is rough on you and I'm sure hit hurts your husband's feelings when he hears that you would rather leave for the day/weekend then spend the time with his children... but I see where you're coming from too!
This boy is going through a lot, he's 3 the world is big and challenging, his parents are apart and Dad's remarried with a new baby. That's a lot for a little guy to handle, but it doesn't excuse his behavior. He's testing his boundaries and trying to manipulate situations to favor his wants. He will only learn that this isn't appropriate if you make a point to show him. It's always more difficult when all of the adults involved aren't working together, doing the same things to set guidelines, but it is possible to break these bad habits even without the help of the Mom. It'll be tough but you've got to stick to your guns and show him that he's not an adult and he doesn't run the show. I don't suggest earphones but do suggest removing him from the situation when he acts inappropriately. Whether you are at home, a friend's house, out shopping or at a park... now matter where you are, safely remove him from the situation and make him sit on his own. Even if it means leaving where you are, cart full of groceries or dripping wet from a pool, enforce the guidelines and don't give him leeway. I would put him in his room, shut the door or put up a gate he can't get around. If you're at the park or what not, put him in his car seat, things like that. Remove him from the situation and tell him this will be where he stays until he can treat you and the rest of the family with respect (explain to him that respect means following the rules and treating people nicely) Make him stay in this place for at least 3 minutes after he has calmed himself. When he comes out take a moment to talk about why he was removed to begin with then drop the subject... he doesn't need to hear about his tantrum all day long, this will only cause resentment and will spur nothing positive. While he is in this 'time out' of sorts, don't punish the rest of the family, go on about doing something fun with the other kids, show him that his outbursts won't dictate the rest of the families fun. If you're at home, play a game, watch a movie and pop some popcorn, paint, etc... show this little boy what he's missing by misbehaving.
I also love charts that not only outline the kids responsibilities (and at 3 he can have household and personal responsibility) but also list good "extras" too. (things like using good manners, doing something nice for mom or big sister, following household rules, etc) I have charts all over my house and it helps tremendously. Each of my charts has a consequence listed if the activity/duty isn't done, each one is set up to fit the 'offense' so they very depending on the item they didn't do or did incorrectly. The extras of course don't have a punishment but everything else does. At the end of the day or end of the week count up the "points" he has earned for each item on the list (have a minimum that he should reach each day by doing simple daily behavior/routines) and have a predesignated reward that he's chosen if he reaches his point goal. (We decide on a goal reward at the first of each month and the points are tallied at the end of each month) Our rewards must be free or very low cost. They are things like making cupcakes, going to the park of the child's choice, play a game of their choice with the entire family, getting to plan an entire meal of anything they want (we get lots of mac-n-cheese with cupcake nights as rewards lol) They also can choose a video rental, buy a pack of baseball cards, or something else that's less than $5. Things like his will help him see his progress and also give him something to look forward to, all while also reinforcing that reward doesn't just happen, it's earned and it doesn't have to cost a lot of money.
I also think it's a great idea to have him go to his father when he arrives home, and even his big sister or anyone else he may disrupt with his tantrums, and make an admission of what he did and why it is wrong... an apology of sorts. This will help him learn to take responsibility and also show him that he has an effect on people beyond himself.
All in all, this little guy needs to know that he can't push you around. So if you begin to feel frustrated, take a moment for yourself but don't let him know he's getting under your skin. I know it's easier said than done, but try your best. In time it will show him his tantrums only exhaust him, they don't get him anywhere. The last thing you want to do is reward his bad behavior by taking him somewhere or giving him something that he wants. He should learn that those things are earned through good behavior not manipulation. I know this is hard to do, please know it won't last forever and once it's enforced consistently it will cause change in him. Heck, these are great things to do with all kids, even the 13 year old. Positive reinforcement also goes a long way. Praise the kids when they do things right, when they do extra things, this will encourage their good feelings about themselves and help reassure them that you care about them and appreciate them. This too will help the situation.
This little boy probably doesn't know how to handle what's going on in his life, simply because he's 3 and matters are made worse by the other changes in his life. He needs you, and his Mom and Dad, now more than ever to show him what's right and what's wrong. Keep your chin up. I am positive that in time, with support and consistent enforcement from his parents and you, this will pass quickly.
Take care,
T.