Per your SWH: Okay then, time to change his poop schedule so that he has to poop in the daytime at daycare. Start giving him prunes and fiber and plenty of water. Talk to your ped about the possibility of Miralax. He's using his strange poop schedule to misbehave and you can circumvent it deliberately with diet. Better do it quick before he ends up in the hospital. Look up what kind of diseases one can contract from poop...
And I'm sorry, but I disagree totally with bribing this child to not play with his poop. He isn't laughing at you because he's nervous or scared. He's laughing because he's enjoying himself. Time to get serious about this.
Original:
DUCT TAPE. Use duct tape on a diaper, not a pullup, so that he can't get it off. And no, don't put it on his skin, in case someone thinks that needs to be pointed out.
You HAVE to prevent this. He could get VERY ill and at 3, he's still too little to understand why he should, though he does know that he's not supposed to.
Good luck.