Both my kids were really high energy/ high needs when they were little. It helped a whole lot to make issues into non-issues as much as possible. It really, really doesn't do any good to have a power struggle with a little kid. It doesn't fix anything! So if there's a power struggle, it's important to look for the underlying needs your child is clamoring to express and look to meet them before they need to clamor.
It can seem excessive! What's "enough" for you may not be nearly enough for a high needs kid! That's important. If there's something about throwing stuff around and making a grand mess that's wonderful to your child then make more of that happen. But that may not be the whole of the issue. It may be that "making a mess" is a good way to get lots of attention - so a good place to start would be to start actively giving your kid a lot more attention. I know that can seem daunting - one of my kids needed an enormous amount of attention when he was little. It was wearing. But he didn't need less when I was done - he just clamored for more. And the best way to get more attention is to do something that pushes mom's buttons. Giving lots of attention proactively ends up taking less energy because you aren't pissed off as much and you feel more in control - you're choosing to give rather than putting out fires.
It's also possible your kid needs a lot of big arm movement in general and throwing things around is a good way to get that. So it's worth looking a more big arm things to do - more things to throw! And some targets to throw them at. Also things to swing with the arms - sticks and swords and bats and rackets. We found an old hand weed-wacker was handy to have around for active kids!
It could be, too, that your kid needs more rough-n-tumble play in general. Moms are sometimes bad at providing that, so you might need to engage some help in that regard. Older kids, teens or adult friends can step up and help. And there's a long list of physical stuff collected here: http://sandradodd.com/physicality/
Someone mentioned a need for control, and given that there's some stress in the family, that's a good place to look, too. Little kids can often feel really frustrated with how much of the world is out of reach, too hard, too complex, out of their control. So it's helpful to them to find ways to feel competent and capable - and how that works is going to be different for different kids. 3-5yos are also fascinated by cause and effect relationships, so those tend to be good ways for them to feel capable. Sometimes that means doing things and seeing/experiencing the effect, sometimes it means getting other people to do things for them. It's not a mean thing on their part - they don't have the development to mess with your head in that way! They're just trying to find ways to feel powerful.
Physical stuff can be good for that - throwing, wacking, even breaking things. But for a kid who likes the social side of cause and effect, games like Simon Says, statue maker, red light green light, can all be good. Also things like having your kid pick your clothes for you, or decide what you should eat for breakfast - things that let them make real decisions but also maybe be a little silly. Ketchup on your cheerios won't kill you
The main thing is to step back from this one issue and try to see what's feeding into it. Behavior is non-verbal communication. The catch is trying to suss out what's being communicated. Your kid isn't trying to drive you nuts - there's something under his skin. He needs help with that.