Unless she has some kind of court order limiting your rights to the children, she is completely out of line with this kind of message. Don't reply until you have talked to your lawyer.

Keep contact with her to a minimum. Maybe get a cell phone for the kids so she can't be the gatekeeper for your contact with them.

I don't know what kind of relationship you had to alcohol before this, but did it impact your job? Your other obligations? If not, she'll have a difficult time showing that you're not a responsible parent, but it sounds like that's the way she's going with this.

M 16 yrs, WH62, P54
3 adult blended kids
EA 11/13, BD1 6/14
PA fall 14, BD2 2/15
Piecing 2015, BD3 12/15
Separated 4/16
WH moved OW in 5/16
Divorced 6/15/17