You need a lot of help. Get out of there and into the shelter ASAP. Have the shelter help you find a lawyer. DO NOT drink from ant contain whatsoever. ""Only a couple" is only a couple too many. You know that already. Go to AA. You will both lose your child if you do not straighten up. I repeat - Get out of there. Get out of that toxic relationship.You cannot appeal an open DCFS can. It is not bogus. Find a lawyer who is experienced in dealing with DCFS . You need one badly. Do not sign any plan or any other document with DCFS.
You really need a lawyer to defend you in the DCFS case. You need yo stop lying to yooourself about the entire situation. Get help now before you loose your daughter.
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An appeal does not sound like it has any chance of success. Aside from the issue of substance abuse by both you and your daughter's father, you have admitted to a history of domestic violence in front of the 11-month old. This in and of itself is enough evidence to support an "indicated" report (and probably a petition for adjudication of wardship) of child neglect based on an "environment injurious" to the welfare of the child. This is so regardless of who the aggressor is in your fights.
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