How can I get my puppy to stop claiming things over my much older dog?

I have a five month old heeler and a much older mixed breed dog. My older dog is VERY calm and submissive, I've had him for most of my life and trained him from a puppy. Lately, I have noticed very undesired behavior from my new puppy such as claiming things (including me) over my adult dog. On several occasions this has led to a scuffle and I immediately isolated the puppy. My main concern is that she could hurt my older dog accidentally or worse, intentionally and I want to prevent that now while she is young and it doesn't become a serious problem later. I know that I need to establish my role in the house as the "alpha" and I feel that I have, but she seems to do this at least once a day particularly when I'm at my desk or sitting somewhere and my older dog approaches me, her food bowl or bag and toys. Some of my friends have suggested moving the food bag or toys so she doesn't have access to them but I feel like that is giving in to her in a way because my role as the alpha is to provide her with these things at MY discretion. Am I doing the right thing by isolating her for a little while? Is there a more effective method I could use to establish that she is not the alpha and claiming is not behavior I will tolerate?