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How old was the puppy when you got him? He is still quite young. Did you see him with his littermates, and meet the mother?
You say your old dog is frail. Several years ago, I had an old rather frail dog and a puppy. The old dog didn't want to play much and she would stop the puppy messing with her, without my intervention. All she had to do was bare her teeth. The puppy loved her and if I say her name, I see that he still remembers her, and not with fear. Doesn't your older dog know how to teach the puppy proper behavior?
My puppy had learned the basics of proper dog behavior before I got him, from his littermates and from older dogs at his breeder's. If your dog missed out on that, then try to find replacements, other puppies, and maybe a stable older female.
My youngest dog now stayed with his breeder and her dogs until he was 11 weeks old. I think that was better than getting him so young.