I was thinking along the same lines as the other poster. If your baby is almost 1, and the inappropriate peeing just started there is something wrong.
Generally speaking, inappropriate urination almost always means illness. Kitty is sick and has no other way to let you know. A UTI is a painful thing and she (he?) blames the litter box for the pain so goes elsewhere.
In a male this can become fatal very quickly, as males have very narrow urethras and can block suddenly, simply from inflammation. Once blocked a male cat will die within 24 hours without emergency treatment.
A female is less likely to block, but the pain is still there.
Please bring your cat to the vet (if possible with a full bladder so the vet can get a urine sample) to rule out or begin treatment of illness.
If illness is ruled out and the problem is then deemed behavioral, then is when you start looking for other causes.
By the way, stress can cause UTIs or crystal formation, and the new baby may have caused this kitty stress, but cats are such masters at hiding illness that s/he is only now getting to the point where s/he is exhibiting symptoms. Meaning the problem may have been going on for some time already.
Please do let us know how things go.