Alcoholic, abusive husband, family wants me to leave

Your situation is painful one, abuse from nobody is alright, least of all your husband and his family. Thank you for reaching out and seeking help, it's a serious decision to make and it's commendable that you're reaching for opinions/ advice.

First things first, nobody can force you to make a choice about your child. Family members can advice, however, the ultimate decision lies with either both parents.
It seems apparent that you're marriage has fallen apart and that your husband doesn't seem inclined to making it work. That coupled with his alcoholic habits, makes it rather difficult for him to make a wise/ reasonable decision about you and/or your child.

In my opinion, your husband and his family need to address his alcoholic habits first. As long as your husband is addicted without any attempt to curb his habit, it seems futile to hope for his effort towards you or your child. Try initiating a conversation with your husband at first, since his family is not being supportive towards your marriage. Try explaining how the alcoholism will not only cause health and emotional issues, it will also deeply affect the child he wants you to leave behind. If your husband is even slightly willing to make an attempt, see a doctor, rehab counselor and begin taking steps in the direction of his recovery. It's a slow process that requires immense patience, but you're willing to give your husband a chance and this is an important step in that.

In the unfortunate circumstance that your husband completely rejects your opinions on his alcoholism/your marriage, it's sensible then to make some difficult choices. The marriage can only work if you both decide to work towards it. It's a two-way street. If your husband wants nothing to do with the marriage, it will be sensible of you to then think about your future and that of your child's.
Getting some legal advice on this matter is wise. Your family seems to support you leaving your husband, and with good reason I'm sure. As a mother, you're the best judge for your child's future and security as well.
It's an extremely painful realization to know that the man you married has now seen his life without you. However, sticking around in such a situation is even more painful and harmful to you and your child.