Its normal. Most often, when you introduce a new cat into a home its best idea to separate the new addition into a separate room for the first week or so. You could perhaps keep the new kitten in your daughter's room. this helps him get used to the new home, and your existing cat get used to the idea of a roomate. Then once you have spent time apart, you can slowly introduce each other at supervised intervals.

We did this to Pouncer and Allen and in two weeks time, Allen had taken to grooming Pouncer and thought Pouncer was his kitten.

Good luck and have fun with the new baby!