Florida child custody law, grandparents' right to seek child custody

Unfortunately, as a grandmother, you have no legal rights to visit the child. If your son is willing and able, HE should file the Petition for Paternity. As long as he has some belief he is the child's father, most courts will allow the DNA test to be sure. If you son is unwilling or unable for some reason to start the action himself (with your assistance, of course), most states allow you to file some sort of third party custody action. These are usually difficult, and most states require that both parents be unable or unwilling to parent the child themselves. If mom is a bad mom or neglectful, this may be an option, but the court will want to know why dad can't have custody first.

Sounds like your best bet is to hire an attorney to help your son get an action started, then get the court to order the DNA test.