With the amount of alcohol sales in the US, I doubt that parents drinking at home while kids sleep is really as rare as many think.
I think she admits to being "drunk" in order to show how she could have slept through whatever happened, even though I am not convinced either way as to what that might be...also to show how "honest" she is.
Now that she's admitted she lied previously, I'm not going to believe anything she says because it is just self-serving excuses by someone who blames everyone else.
JMO