Ideas
I have had this issue recently, the parent Sims repeatedly picks up the infant, autonomously and randomly inserting "pick up infant Sim" into their action queue, and then they either just put the infant down or hand the infant to another Sim, often while the infant Sim was trying to sleep.
I have also found that the parent Sims will not always feed the infant Sim when told to do so, nor will they put the infant Sim in the crib when told to do so. They often cancel the interaction or stand around the infant Sim doing nothing. This interaction succeeds more often if I pick the infant Sim up first and then try adding the action to the queue.
I have also had the parent Sims both often freeze up in place when talking to the infant Sim. The only way to unfreeze them is to the cancel the talk to infant Sim interaction. Neither the parent Sim nor the infant Sim moves when this glitch occurs.
I have had five children raised from newborn to child/teen in this current save and the fifth and most recent infant Sim really had the most instances of needing to be picked up first to be fed or put in the crib. Both parent Sims refused to feed this infant Sim multiples times for so many times in a row that I had to cheat the infant's hunger need away (fillmotive_motivehunger) to prevent it from being taken away. The parent Sims successfully fed the other four infant Sims and started being able to feed the fifth infant Sim but after 1-2 Sim days they continuously cancelled their actions to feed the infant Sim.