I had the same issue. The notification said the task was finished but I could not select new tasks for the parent sim nor the infant sim. I could not even get the parent Sim to pick up the infant sim and put her back in the cot to end the "follow obsessively" task. I fixed it by selecting the map and then selecting another Sim's house. Then I selected the parent Sim in the Sim Tracker while at that house and from there sent the parent Sim to work. When I went back to the parent Sim's house the infant Sim was back in the cot (crib) and the task was ended.
The nany appears outside of every house for me too, but only goes inside houses with infants.