Toilet Training - I need a Trainer!

I have no idea what I'm doing when it comes to potty training. Zero.

And the internet doesn't do anything except make me feel more conflicted about how to approach this endeavor. I've read blogs, parenting websites, watched youtube videos. I still know nothing about potty training.

Case in point: I've been trying to have Lucan run around the house without pants and a diaper. Lots of peeing on things that aren't the potty. One day I changed his shirt because it was soaking wet and he insisted on wearing a onesie. A white, Iowa State onesie in which he then insisted that get snapped at the bottom (I tried to leave it unsnapped but he kept doing head stands and somersaults in trying to button the snaps himself. It was pretty funny so I finally took pity on him and snapped him up). Two minutes after snapping the buttons, Lance asked me if I smelled poop. At the time I didn't. Then Lucan entered the room and announced "poop!" Lance proceeded to ask Lu if he needed to poop, but it was too late. Lu had already pooped in his onesie and used the snaps as a poop hammock. That was a fine moment in potty training.

But here are the few things that we're doing and I have no idea whether they are right or not.

• I bought a frog potty a month back when he started being interested. I figured it couldn't hurt. He had been taking off his diaper for a long time at this point. 
• At daycare Lu saw everyone using the potty and he wanted in on the action. 
• At daycare he will go on his own, by himself. He won't do this at home. I have to basically beg for him to use the potty. 
• On the flip side, at daycare Lucan has been caught trying to flush an entire roll of toilet paper. Twice. He doesn't do this at home. Daycare provider's exact words "He's sneaky, fast." Yeah, I know. 
• If he successfully uses the potty, Lucan gets three M&Ms. 
• We've installed an order to pottying - first potty, then dump potty, flush, wash hands and then TREAT. Lu understands the concept of treat pretty well. He likes to run around the house yelling "TREAT!" at the top of his lungs. 
• At home we let Lucan go diaper-less and pant-less. This is supposed to help lessen confusion and help them understand when their body is telling them to go. All I've seen is an increase in pee puddles. 
• If Lucan poops, I give him extra M&Ms. Because poop is worth a party full of M&Ms.
• Positive reinforcement only. If Lucan has an accident, I don't scold him. That being said, Lucan peed on the floor intentionally the other day. Lance made him mad and Lu looked him square in the eye and started peeing. Awesome.
• We still diaper during naps, at night and if we're going somewhere or have people over. This probably isn't helping Lucan learn. 

OKAY. Someone tell me what to do next!!