I have seem plenty of questions and posts about how could Superman (with all his powers) deal with XYZ, more or less having his Superpowers in the way of everyday routine for a normal human.
Probably one of the most famous would be "Man of Steel, Woman of Kleenex" which explains the problems Superman, due to his biology and superpowers, would face in a situation where one (mostly) loses control of processes that are not completely controllable take place. If I recall correctly, this is even explicitly mentioned in Superman Earth One.
Anyone in care of a baby or toddler knows that at times babies or toddlers can be quite physical. At least, they are very physically demanding for parents! They are not yet able to communicate effectively, and thus their frustration may manifest not only by screaming, but by more physical behavior when they are upset (which can be quite often, even if it is for short periods of time). They might mistreat their toys, throw stuff away, resist to be hold, bathed, fed, changed, put to bed, etc.
We have several alternate Supermen (Movies or cartoons, different lines of comics, etc.) but what seems to be "canon" is that Superman is rescued as a baby by the Kent and even at that sort age he is exhibiting some of his superhuman abilities. Depending on the storyline these abilities might show or increase over time, but other seem to be there from the very moment he is exposed to the yellow sun.
Comics, by nature, expect some degree of suspension of disbelief. Nevertheless, Superman's strength seems to be there when he is a baby, and I can't imagine the Kents having to deal with a baby who is much stronger than any adult, presumably much faster (if he wants to escape a diaper change or bath time) and who knows what else.
Is it ever addressed, in any canon, how Jonathan and Martha Kent deal with a super-baby?