If a parent does not want to voluntarily transfer custody, then she can be made to do so involuntarily by a court of law. Like most states, Florida family law
does allow for a third party relative to file a petition with the court requesting custody. The court's sole concern is what is in the best interest of the children.
Keep in mind, there is a strong presumption in favor of parents. As a result, the court often begins from the point of view that a parent should have her own children. It is the responsibility of the person who is petitioning the court for custody to show that circumstances with the parent would be so detrimental to the children that the parent should not have custody or that the parent does not have the ability to care for the children or provide for their basic necessities; in other words, that the parent is unfit. Short of permanent custody, however, the court may also award temporary custody, depending on the facts, and subject the parent completing certain benchmarks before getting her children back (such as obtaining housing, employment, completing parenting classes, drug testing, and so on).
Contested matters involving minor children are best handled with the assistance of a lawyer. If you cannot afford a lawyer, you can always apply with your local legal aid office, as they provide representation at no cost. If you must handle it on your own, you can still retain a lawyer for limited representation in helping draft the paperwork and providing advice. You can always contact the clerk of the court, because some courts do have self help centers and blank forms that can be used as guides, and another source would the legal forms found in the legal section of the library.