Thank you everyone for taking the time to give me advice on this matter. I will definitely stick to redirecting rather than laying her on her side first. I'm glad to hear this isn't a sign of an aggressive dog. It certainly didn't seem like she was playing as the first time it was over my older dog's food dish and the second scenario could have been territorial of the space on the couch with me. Her tail wasn't wagging at all and her bark was different, but we are just getting to know each other and we certainly could be misreading the behavior.
Ideally, we would have waited until our old girl passed to get the puppy but my husband is an on-call firefighter who is gone all hours of the night and his full time job is ramping up his travel schedule this year. With little ones at home we needed some protection. There have been some break-ins in our neighborhood recently, leaving us feeling a bit vulnerable. My family has been trading off time with our old girl one on one while the others are with the puppy so she doesn't feel isolated or replaced. Thanks again for the help!