The Department (DFCS) has the ability to remove your children from your care. At a deprivation hearing, the State would have to demonstrate by clear and convincing evidence that your daughter is without proper parental care or control, subsistence, education as required by law, or other care or control necessary to sustain your daughter's physical, mental, or emotional health or morals. A finding of deprivation also requires proof that the deprivation resulted from unfitness on the part of the child's parent, which unfitness can be the result of intentional or unintentional misconduct that leads to the abuse or neglect of the child or some physical or mental inability to care for the child. If you allowed your boyfriend to continue to come around the children, the Juvenile Court could find (if your kids were subsequently taken into custody and a deprivation petition filed) that your children are deprived in that you failed to protect them from someone (your boyfriend) who the State seems to believe either hurt them or presents some untenable risk to them. So my colleagues are correct - this is a matter of priority. You have to decide who comes first - your boyfriend or your daughter. Best of luck to you.
This answer is offered for informational purposes only. It is not offered as nor does it constitute legal advice. This answer does not constitute an attorney-client relationship. Do not rely on this answer in prosecuting or defending against any criminal or civil legal action. Speak to an attorney in your area about how to protect yourself and your interests.
The simple answer to your question is, of course, no. They cannot "kick your fiance out of your house." However, the control they have is over you and their ability to remove your child from your home. Apparently, they gave you the opportunity to keep your child, so long as you complied with their condition - that your fiance must leave. You should be grateful for this opportunity. They could have just removed your daughter, no questions or conditions.
What you should be questioning right now is not what DFCS can do, but what you should do to retain custody of your child.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
It sounds as if your fiance may be a danger to your child. (DFCS's requirements really makes me wonder what your fiance was on probation for.) So though they do not have the power or authority to kick him out of your home, they do have the power and authority to prevent him and your child from living under the same roof. Their means of doing that would be to remove the child if your fiance lives there.
Apparently you can only live with either your daughter or your fiance, not both. You need to decide which relationship is more important to you. Because apparently you cannot have both. (At least not until your fiance convinces DFCS that he is NOT a danger to your child.) You need to protect your baby. If you won't, the state will take her.
The above answer is a general explanation of legal rights and procedures. It does not constitute legal advice. Nor does it establish an attorney-client relationship between the individual posting the question and the attorney providing the answer.