Excellent advice from Ajshep there. I'd just emphasise one of his points. Do the things he suggests only, as he says, "if intervention is needed". The fact that your older dog is telling the pup off when he gets too boisterous is, in fact, the best way for your pup to learn that his behaviour is wrong. Most older dogs will give a bumptious pup a sharp snap to put him back in line - usually this is just noise and in most cases the pup accepts the reprimand as a normal thing to happen and is fine a couple of minutes later. Unless the situation develops beyond this - ie the pup not heeding the reprimand or your older dog is becoming distressed by the pup's actions - then there is no real need to intervene.

I agree with Jackson - please don't use a water pistol on a puppy of this age. And I too have never seen a mum nip her pup on the neck - I've seen a mum give a pup a quick snap as I've described above, but that's different from nipping the neck.