Angelo writes, "I was convicted with felony, I did my time, and now I am trying to go on with my life, being a good man, father, and husband. I would now like to become an American citizen. Am I allowed to?"
Absolutely not. Actually, it is surprising that you have not already been deported. The legal system is not perfect and there are still gaps in information, otherwise, when you were arrested first or at some point in your criminal journey, someone failed to contact ICE and report your situation. Convicted felons are summarily deported and are definitely not eligible for naturalization. It also seems that no exceptions can be made even if it causes enormous suffering to your family. If you want to be together with your family, they have to relocate to your native country. You may still want to hire a competent immigration attorney to assess if something can be done in your case and in the meantime you should not leave the United States, because when you return your green card will be revoked and you will be sent back forever.