No such thing as too much posting in this forum,
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I also believe in truth as much as possible in an age-appropriate way. At 6, yes, DD knew that Dad was "sick" because of alcohol & that it was not the same kind of "sick" that she understood. That is wasn't something she could catch or that he could just take medication for but that kept him from being healthy just the same & affected the way he sometimes made decisions. She was the one who filled in the blanks - "you mean like the way Dad gets pulled over by the cops for speeding all the time or is really late picking me up or cancels plans?" Once I started asking her about the things she thought, I really didn't have to do a lot of talking.... she had noticed the moods, the yelling, the everything. So much more than I had anticipated.
Definitely worth consulting an attorney for legal advice & filing a police report if you haven't already.