A few things:
The "terrible twos" isn't infancy. The word "infant" comes from the Latin
infans, which is literally in + fans, (not + speaking). So, my comments are being restricted to a narrow window that generally disappears within the first 2 years of life.
Sin is connected to rationality because sin must be against law, either natural or positive. Natural law is directed to reason. That is why wolves and parakeets don't sin, though they might do things that negatively affect others. Following instinct, automatic reflexes, and natural responses is not culpable.
Looking at infant behaviors, such as crying, as sinful is importing adult standards of behavior back into children. Many of these behaviors are inborn reflexes, merely stimulus-response mechanisms. For example, many child development psychologists see the earliest "fussy" behavior as a way that infants develop attachment and build trust. For example:
http://www.childcarequarterly.com/pdf/fall10_babies.pdf
Also, discipline at very early ages can be tricky, since babies aren't actually born with cause-and-effect reasoning skills. They literally may not make the connection between "no" and a negative evaluation of their actions. I'm not saying this for 4-year-olds, but quite probably for 12-month-olds, and it's even possible that some of the "terrible twos" may be linked to this phenomenon.
To sum up:
1) In the Pelagian controversy, despite all the disagreements, all sides agreed that infants do not commit actual sins.
2) The Old Testament sacrificial system points to a distinction between an always-present sinful propensity and discrete transgressions.
3) The NT commands to confess sin do the same.
4) Psalm 58:3 seems to support the distinction, since the example of "going astray from the womb" (original sin) is "speaking lies" (actual sin of a post-infant person).
5) Infant behavior must be interpreted within an age-appropriate biological and psychological framework, not by drawing analogies to adult behavior.