Babysitting, dear, is one thing. The stress of having your own--which can often mean not getting any rest and not having a chance to escape even for a moment, for years on end--is quite another. For people with issues coping with stress, loud noises, major disruptions of routine, etc. parenthood can (in certain cases) be extra challenging for those with AS. Even NTs are typically astonished at the level of stress involved, especially in the early years.
One of my biggest problems is having to talk constantly. Although I'm really good at talking to myself, I'm generally a quiet person. I don't like talking, except in very rare cases. I actually feel tension just from having to open my mouth and form a thought into words. Now, I've had to adjust to giving non-stop instructions, "Do this", "Don't do that", "Get your finger out of your nose", "Stop hitting your sister", etc., etc... I find myself tripping over my tongue all the time. You have to figure out how to explain even the painfully obvious, in simple language, one step at a time, giving gems of advice along the way, "It'd be easier if you took your head out first..." And you can never be in all places at once. It's not always so easy.