Totally agree with llombardo usually they have a "tell"
Anything from tensing the whole body, staring, or even just a wrinkling of the brow. My first dog was very dog aggressive, we did a lot of work with her and yeah finding her "warning" was so important - once I had it I could mostly divert her before anything bad could happen. (with her it was 2 wrinkles would appear between her ears as she got attentive) toward another dog.
With your golden "guarding" his puppy - he's not allowed to do that, while you are there it's YOUR responsibility not Sams to keep puppy safe. ATM Sam is taking leadership over both of you and in my book that's not acceptable.
The fact that the snapped at the other puppy is bad but also - he snapped AT it - if he had have wanted to he could have grabbed it and shaken it in a split second.
The puppy yelping and screaming and running away is also normal - it's how they defend themselves. It's letting the other dog know "I'm only a baby don't hurt me" - it sounds awful lol you'd think someone just cut their throat.
If I was you and I wanted to take both of them to the park together I'd get someone (ideally your partner if you have one) to go with you. One of you to watch over the puppy, the other one to take Sam on lead away from the puppies and just do some really basic walking and perhaps a few sits and drops (for food treats) - you demand Sams attention, he's supposed to look to you not the puppy.
If you are worried about him hurting another dog - get a muzzle - better safe than sorry and it will allow you to relax a little and not be so tense as he will pick up on that.
Even if you get him a "cute" pink muzzle
I think getting a behaviourist or a trainer may be a good idea just to give you a bit more confidence in handling the situation - sometimes it's nice to have some "backup" someone that knows how dogs work and don't think that you are the worst person in the world because your dog happened to growl or bark. So many people at dog parks just have no idea and get all rude and offensive.
How old is your puppy?