Can I file at the US Embassy for reentry permit for all of my family?

You appear to have lost your right to permanent residence by not having returned to the country since 2007. If you and your family attempt to reenter the States with your green cards, you will likely encounter problems with Customs and Border Protection once it understands that you have been out of the country for so long. A reentry permit can only be legally applied for while you are in the country. As you no longer have a right to come to the US with your green cards, your third child also has no right to enter. It appears that you would have to go through the immigration process all over again in order to come to the US as immigrants.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

Since you have been gone for so long, the law treats you as having abandoned your permanent resident status.  You have to maintain a permanent presence in the US to keep your green card.  You may attempt to return using a returning resident alien visa.  Here is a link with more information.  Of course, your newest child will not be able to travel with you.  You will have to file a petition for that child and wait for it to be adjudicated to bring the child with you (assuming you are granted the returning resident alien visa). http://travel.state.gov/visa/immigrants/info/info_1333.html