We run here, too. In fact, dd has been starting to run laps around the house when she gets crazy. I don't tell her it's because she's crazy, I just say, "okay, go get your shoes!" and she does all excited and runs her laps while I "time" her. She thinks it's great, and comes back in all red in the face, smiling, and...much calmer. (c:
16 months is pretty little. One of the things I do when ds pushes and shoves against me is I say, "If you push Mama, you will fall" in a not harsh but very serious tone. Then when he does it again, I quickly plop him on the ground, and even give him the sensation of falling (although he's not hurt in the slightest...I just move really quick and give him the feeling of weightlessness), and I step back. Then I say, "When you push Mama, you fall down. Don't push Mama." And I pick him right back up. It never takes more than 3 times when he's going through a spell of it before he stops pushing me.
I truly don't believe that socializing, especially a young toddler, is important at all. So, I'd just stop playing with other kids if I could. I won't hold a kid who hits me. No talking about it, no nothing. Just see ya later. So, I'd plunk him down out of reach and tell him you don't play with people who hit. I'd do it over and over...refuse to let him near me if he was hitting me. (With one that young, the whole ordeal would be over in about 20 seconds, and we'd be cuddling again, until the next time. "plunk. mama doesn't play with people who hit.") He'll be surprised you don't feel like lecturing, and I'd scoop him right back up and move on to something fun. Again, I'm pretty matter of fact. And it's not really something to make abig deal out of. We just don't hit. Plunk. I don't feel like it has to be an emotionally charged event...he's not headed for jail on charges of assault. I think kids feed on our emotions...if we're tense about something, they will be, too. He can sense this is a really, really big deal to you. So, I wouldn't let it be, just, again, I'd be matter of fact and the let it be over right away and make sure he's enjoying a fun time with you, not just bored on your lap being invited to hit again.
Oh, and I wanted to add that MY experience with animals is that when the puppy nips the mother, the mother NAILS the puppy, leaving no true injury, but also no doubt who the boss is. It's not about teaching empathy in the animal world...it's about establishing authority...bigger and badder, so to speak. I think a better way to teach empathy...if your ds were 3 and not only 16 months...would be to show him times when someone/something hurts something else or takes a toy, etc. You can really start to talk about feelings, I think, after you've had success helping your dc identify their own. Until then, it's all just words, and at 16 months, I'd guess he doesn't have many.
"If you keep doing the same things you've always done, you'll keep getting the same results you've always gotten."