You could hire private attorney and file to terminate his parental rights based on abandonment. Go talk to a family law attorney before you do anything else.
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You should definately hire an attorney to assist your current husband in the adoption of your child. Your case brings up an important issue that must be addressed proactively - Sailors & Seaman's Act -- there are special rules in terminating a parent's right if they are in active duty in the military. You should address this with your attorney and make all effort to comply - otherwise you adoption can be voided.
Secondly, you say that he has not been active, but yet refuses to consent. A good adoption attorney will contact the birth father and give him an opportunity to explain himself. Often men do not want to put anything in writing showing that they have abandoned their child - lots of guilt. Frequently, I will ask a birth father to write a letter to the child - this lettrer is given to the child many years later and explains that although he loved the child, he was unable to care for him - this way it is a loving act. I have found in my 28 years of adoption law, that many birth fathers respond positively especially if you show them a little respect.
You should make every effort to obtain the biological father's Social, Medical and Family History -- it is the best thing you can do for your child. His future may depend upon it. keeping the door cracked open can lead to future valuable information regarding a child's health.
The facts appear to be on your side. A good adoption attorney in Florida who is sensitive to the rights of biological father's will be able to guide your case through the Florida law, procedure and court. Remember only the judge can terminate the rights of the birth father. With him being in the military - it makes your case even more delicate.
Wish you and your family the best
Consult with an attorney in your area. The biological father must consent. Going after him for child support is a good step in the right direction. If he doesn't pay, he can be held in contempt.
R. Jason de Groot, Esq., 386-337-8239
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