How to get divorce from alcoholic partner with no visitation rights?

Assuming you are a Hindu, you will be governed by Hindu Marriage Act 1955, Section 13 of the Hindu Marriage Act provides grounds for dissolution of marriage.

Section 13 is reproduced here under for your understanding:

Section 13(1) states that a petition may be presented by either the husband or the wife, for dissolution of marriage by a decree of divorce on the ground that the other party-

i. has, after the solemnization of the marriage, had voluntary, sexual intercourse with any person other than his or her spouse; or

a. has, after the solemnization of the marriage, treated the petitioner with cruelty; or

b. has deserted the petitioner for a continuous period of not less than two years immediately preceding the presentation of the petition; or

ii. has ceased to be a Hindu by conversion to another religion; or

iii. has been incurably of unsound mind, or has been suffering continuously or intermittently from mental disorder of such a kind and to such an extent that the petitioner cannot reasonably be expected to live with the respondent. 

Explanation.- In this clause,-

a. the expression" mental disorder" means mental illness, arrested or incomplete development of mind, psychopathic disorder or any other disorder or disability of mind and includes schizophrenia;

b. the expression" psychopathic disorder" means a persistent disorder or disability of mind (whether or not including sub- normality of intelligence) which results in abnormally aggressive or seriously irresponsible conduct on the part of the other party, and whether or not it require or is susceptible to medical treatment; or

iv. has been suffering from a virulent and incurable from of leprosy; or

v. has been suffering from venereal disease in a communicable from; or

vi. has renounced the world by entering any religious order; or

vii. has not been heard of as being alive for a period of seven years or more by those persons who would naturally have heard of it, had that party been alive.

Therefore, in view of above mentioned section, you may file a divorce petition under Section 13(1)(a) i.e cruelty which includes mental and physical cruelty or any other ground which you feel can be fitted in your circumstances.

Furthermore, with respect to custody of your child, your child is minor and that you need to file a petition for the custody of the children. Section 6 of The Hindu Minority and Guardianship Act states that the ‘natural guardian of a Hindu minor, in respect of the minor’s person as well as in respect of the minor’s property  in the case of a boy or unmarried girl is the father, and after him, the mother, provided that the custody of a minor who has not completed the age of five years shall ordinarily be with the mother.

In your case, your child is 1 year old, so, in view of aforesaid section the Court will allow to retain the custody of your child.

Further with respect to visitation rights, you will have to mention in the above petition that father shall not be allowed visitation rights because of welfare of the child. 

Depending on the facts your case or evidence, the Court may deny visitation rights. There are various occasions wherein Court has denied visitation rights to father, in the interest of child.