I assume that the OP bought a separate seat for her baby if she plans on using a car seat?

I ask because on a full flight a while ago, I arrived at my seat near the time the door was to close only to find a baby in his car seat. The mother said that she needed to put the baby there for safety reasons. I didn't question the need for a car seat but I did say that she needed a seat which was not mine and I showed her my boarding pass. She refused to move the car seat. I found an FA to make this woman free up my seat. He reminded her that if she thought her son needed a car seat for the flight, she should have purchased a separate ticket for him. I got nasty looks from the mother the entire flight but the baby smiled during much of the trip he was awake.