I live with my mother for the time being. Initially she suggested that I get a puppy now before I move out so that it can interact with my mom’s dog and they’d get to know each other before I moved out so that we could visit her with the pup in the future. To that end I found someone selling puppies and inquired.

Now she has changed her mind and is afraid that a new puppy may cause her dog to pee all over the house in order to “mark his territory”

is this a real thing that happens? If it is, are there steps to prevent it from happening? Should I just give up on having a puppy for now?