Opinions? Am I a terrible person?!

I'm posting this anonymously because I feel like a terrible person and I guess I just need opinions on if I'm really being terrible or if its the hormones making me feel this crazy. My husband and I are giving our parents their first grandbaby and his grandparents first great grandbaby. They are ecstatic. My mom calls my daughter "her baby" and his mom and grandparents have made similar comments talking about how she will be with them all the time... I know, I have nieces and nephews from my step sisters.. I call my nephew "my baby" and I tell me sister all the time I would just adopt him in a heartbeat. I know it's because they are excited and they are going to love our little girl so much. But I'm a pretty insecure person I guess and I'm so worried my baby girl won't like me. Or shell want to be around them all the time and not us. I'm typing all this out thinking I sound terrible and completely ungrateful for such a loving family. I'm so thankful. I am. I'm just also a push over and afraid I won't stand up for what I want for my daughter because I don't want to hurt anyone's feelings. These hormones are really getting to me y'all. 😭