if she is illegelly in the country then she WILL get deported if found out, but as far as im aware if the child was born in this country then you are the legal guardian ( unless your illegal to???) she can go to court for her child but again thats not what you want,
she cant just come and take the child when ever she pleases, she needs to think about the childs needs, if the child is settled then its wrong for her to do this, plus if she gets arrested or found out where does that leave the child??? with the new boyfriend????
i think if i were you, i would be heavy handed and explain the child is settled with you and that if she doesnt stop upsetting the situation you will seek legal advise which may lead to her being deported, sounds harsh i know, but if the child really is better off and settled with you it needs to be done.
i dont understand anything about illegal imigrants, i dont know why they come and laws about it so i shouldnt comment, but i think coming over and getting pregnant twice is a bit silly coz like i said before as far as im aware if she gets deported the child will not automatically go with her, so she could loose her children and have to fight to get them back,