I have only seen the phrase "littles" in two areas of use.
1. An old 80's cartoon that has mostly fallen out of pop culture memory.
2. From pedophiles frequently discussed in this forum. I have never seen a normal adult in the current year use it. This is why you hate it and it sets off alarm bells.
Personally I would give the former nanny a pass. Likely a girly rural childless usage of the word.
Yes, doctors may prescribe alcohol, even today. As far as I know, the only legitimate use for it is for alcoholics. Some alcoholics are too far gone to go cold turkey and need to be weened off booze. Yes, they can in fact die if they are completely cut off all at once.