Also are strollers allowed in palaces or moorish castle ? At the moorish castle it will have no use, impossible to use it along the walls, in Pena Palace if it's crowded no space to maneuver it. Also if the buses are crowded I can't see how you could carry it inside. To be honest with a small child I would stay in town, go to Quinta da Regaleira and if you feel like visiting a Palace, visit the National Palace in the center.
Even Quinta da Regaleira is undoable with a stroller, I'd say. There are narrow and uneven stairs, it's hilly and dusty. Not to mention that unless a private car takes you directly to the entrance, you have to walk for several minutes next to the main road on an extremely narrow sidewalk. It's dangerous and unpleasant for one person, let alone a person pushing a stroller.