MB here. If you were interviewing with me I would fully respect some edited version of this - basically tell the truth. That this was your first experience as a nanny with a mother in the house full time and it just isn't the best fit for you. (This assumes you won't be interviewing for these kinds of jobs of course.)
No badmouthing your current employer of course, but I think it's reasonable to tell a prospective employer that you've learned that a better fit for you would be where the parents work out of the home, or whether they have fully separate work space that doesn't infringe on the infant's ability to sleep, maintain a schedule, etc...
I wouldn't dwell on it of course, but I think there is a way that you could tell the truth that is professional, appropriate and that a potential employer (especially one that would be a good fit for you) would respect.
Acknowledging that you take the commitment seriously and will be giving very significant notice, helping find a replacement etc... will also speak to a potential employer (or would to me at least).
Of course, the minute you give notice your current employer might see the light and try to make changes that make it more tolerable/reasonable for you. You should be prepared to consider whether there are changes that would allow you to stay or not, before it comes up.
Good luck!