rights of illegal mother

can a woman that is here illegally and has a child from a u.s. citizen and the child is a citizen take the father to court for child support? she is working here illegally and is afraid that she will get deported if she goes to court but wants him to pay child support. she receives welfare for the child and they are pushing her to give the name. does she have the right to take him to court? and what will they do if they find out she is here illegally and working illegally? please someone advise, i don't know what to tell her, she is my neighbor. thanks in advance.

Good news, I say! If she can prove that her child IS the child of an American and her, as you had stated, then I seriously doubt she whould be deported. Her child, if born within the confines of the USA, is now an American citizen. Only thing is, she has to give his name and he has to be tested if he refuses parentship of the child.
Best of luck