I'm aware that a double negative like in
I didn't do nothing that day.
to emphasize that you really didn't do anything that day is not standard English. Yet, I thought it's quite commonly used, but that may differ regionally. Today, I used such a double negative combined with "neither". Similar to:
Kid: Mom, can I have a cookie?
Kid: Or can I have a piece of cake?
Mom: You can't have neither.
My colleague who is a native speaker (I am not) said that Mom's statement is completely wrong.
Now, my actual question is: is there something about "neither" which makes it less acceptable in a double negation, compared to the first statement I provided? Even though I wouldn't use neither nor in a negated sentence, Mom's statement seems pretty clear to me. Knowing that a formally correct reply would be: "You can have neither." or "You can't have either" - as pointed out in the comments.
In addition to the original question:
This made me head scratch some more. If mom were to respond to the kid's request:
No, you can't. Neither cake nor cookie.
That would also be correct in standard English, right? But putting this together into one sentence would then become:
No, you can't have neither cake nor cookie.
would it not? Is this a valid sentence in standard English?