K1-Visa

Your US Citizen fiancé can sponsor you and your 16 year old child for Fiancé visas, and once you enter you have 90 days to get married. Thereafter you can both adjust status to get your green cards. You can return to your country while the case is pending only if you apply for an advance parole document. The purpose of the advance parole is to visit and then return. 

Your plan appears to be fairly ambitious. While it may be possible for the events to unfold in the way that you would like, be advised that an adjustment of status process in the US from K-1 status could take upwards to a year and you are not allowed to travel unless you have special permission – advance parole – which can take over four months to obtain. In addition, going for a marriage based green card presupposes that you have a bona fide relationship with your spouse, and that might be more difficult for you to prove if you are returning to work overseas rather than establishing a married life in the US. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (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.