I always made sure my kids knew that they were more important than our dogs. The reason for that was that once we got a dog, it seemed like my mother liked the dog the most. Of course, I was a child at the time, and didn't realize how much of a Mother Bear my mother could be about her kids.
I also remember worrying that I wouldn't love my daughter as much as my triplet sons, who were 1.5 years old when she was born. I knew I'd love her, so that wasn't the issue. Of course, I love all my children to the moon and back. OTOH, I also worried about how to take care of a girl baby, I was so used to boys. That wasn't at issue either. Thank goodness she didn't care if I dressed her in several different pink outfits a day. My friends got a little crazy with the pink, they were so thrilled I'd had daughter. (My cousin, OTOH, has 5 boys, including triplets.) I made the most horrible comment to her when she bought the baby to my aunt's house. I said something along the lines of "I hope you aren't going to try for a 6th baby, hoping for a girl". I am still embarrassed about that - it just flew out of my mouth, for no good reason.
I used to tell my daughter's boyfriends to remember that we have two sets of triplets in the family, and that I am an attorney. I was hoping the idea of having triplets would scare them away and keep their paws off her. I only liked one of her boyfriends, and at 26 years old, she's had a lot of them. I had good reasons for not liking them. The worst too told her they had been having frequent thoughts of killing her. She didn't tell me that, ever. Her brothers told me. The kids kept it from me because they were afraid I'd commit homicide or call the police. It sure made me angry enough to think about it. My sons took care of it by making sure the guys were history (in my daughter's life).