single mother seeking divorce and maintenance from separated husband

Assuming you are hindu,
You can seek divorce under section 13 of the Hindu marriage act.

Section 13 of the Hindu Marriage Act which covers divorce has been reproduced below for your better 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.

So as per the above mentioned Section, you can seek a decree for dissolution of marriage (divorce) on any of the above mentioned grounds.

Depending upon the facts of your case, you can file for divorce under section 13(1)(ib)

Now regarding your second query,
you and your child are entitled to maintenance from your husband.
Along with maintenance you are also entitled to back the stridhan i.e. the gift and other things that you brought with your self in your matrimonial home.

Also, your child is entitled to share in his/her father's property.