I traveled here to the Dominican Republic in August on a business trip which has extended longer than I expected. Since my mother became a US Citizen while I was a minor in the state of New Jersey I applied for my Citizenship Certificate but it has not yet arrived. My permanent residence card expired last month. What can I do in order to return home? Thank you in advance for your answer.

You should have applied for a U.S. passport before you left the U.S. You are a U.S. citizen and is required by U.S. law to enter and leave the U.S. with a U.S. passport. You can apply for a U.S. passport at a U.S. consulate abroad. You will need the same proof that you used to apply for the Certificate of Citizenship: your mother's Certificate of Naturalization, your green card, proof you resided with her before you were 18.