Be civil and discuss your terms with your Child's Father concerning visitation and financial aid. If they refuse to hear your terms, you may demand for custody.
Just make sure that there is no reason for the other party to deny your right against the child if they will take legal actions against alleged foul relationship with the grandfather and if they will argue that you are not financially equip to raise and maintain the child's medical needs if there is.
No less than the Supreme Court of the Philippines enunciated that the parental authority of a mother over the person of her illegitimate child may be taken away from her and awarded to another person due to some compelling reasons such as neglect or abandonment, unemployment, immorality, habitual drunkenness, drug addiction, maltreatment of the child, insanity, and affliction with a communicable disease that would render her unfit to perform her duties as the custodian of the child (Joey D. Briones vs. Maricel P. Miguel, G.R. No. 156343, October 18, 2004).