I think when they are 3 you can drive yourself crazy trying to stop the stimming. Keep in mind that there may something very real, serious and often biological behind it. I don't think you should not try to redirect your 3 year old, but I do think you have to approach it with a realistic expectation about the possibility that your child may not be able to stop right now.

There are 2 different approaches to this. One says we must try to decrease stim behaviors through various repetitions and rewards/aversives. The other would agree with CBP who said that the stims have a purpose and are oftentimes anxiety driven. Through the Autism Treatment Center of America I heard of a girl who did alot of hand flapping and guess what? They took her to a good eye doctor who explained that she was actually using that behavior to manage visual input so that she could process it better. There was actually a physiological reason for it! I take the social communicative approach because the through the stims I was able to communicate my love and acceptance to my son and really build a connection to him that makes sense to him. They can and do stop when they no longer need those behaviors to manage anxiety or they grow out of the physiological reason or if it has to do with digestive issues or managing sensory input.

My son is now 24 but I can relate. My son used to flap his hands constantly and to be fixated on clocks. (Age 5,6 and 7) If we tried to stop it, it would cause more anxiety. So we allowed him to do it for a little while and then re-directed him. He used to be fixated on digital clocks and would watch for what seemed forever and flap his arms...I would let him do this for about 10 minutes and then re-direct him. In fact one Halloween, I decided to make him a clock costume since he related to clocks so much and it was the first Halloween that he actually enjoyed. Eventually through re-directing him and getting him interested in other things, the flapping lessened until finally it was gone.

I figured out that when DD stimms it's because she needs solid input. I bought a fairly heavy weighted massager and plugged it in. The constant buzzing and the weight of it instantly soothes her when she's just too much and I need a breather.

At three don't worry about the mild swimming behavior yes you shouldn't let it be the only thing he does but for 5mins now and again there is no real harm. Depending on the types of swimming behavior present you may want to redirect it to appropriate actions. IE chewing on a chewable necklace, spinning tops, spinning on swings etc. but the hahavior itself should never be punished.