If you divorced before your 10-year card was approved, and didn't apply for an I-751 waiver, that could cause big problems.
Otherwise, if that's not an issue, you may still have to answer some questions about your marriage. Bring the divorce decree and your child's birth certificate to the interview. If the other parent of your child is the same ex-spouse who petitioned for your green card, you probably won't have much explaining to do about your marriage. But if your child was conceived during your marriage with somebody other than your spouse, be prepared for trouble.
To give you a better picture;
2001 entry
2001 Marriage
2005 GC approved (10 yrs)
2005 Child born (From US Citizen Spouse)
2008 Divorce
I was married for 7 years. My ex wife (petitioned for green card) is more than willing to vouch for me. I have stayed a committed dad. In fact, my child is the sole reason for staying and making it here. So there is no bad blood nor any suspicions from my ex wife or her family. She would be willing to come to the interview if need be.
I have followed the rules, when I moved I filed an AR-11 (correct me if I am wrong). I even have gathered and kept proof of mutual investments such as bank account statements, pictures, etc. No criminal record, no bad credit, employed with same employer in all those years. So I have no fear of answering questions because I would not be hiding anything.
The whole reason I started worrying is when I went to my home country 2 years ago, when I came back into the US, the immigration officer at the airport gave me such a hard time. He warned be about renewing my Dutch passport. It was still valid but about to expire. The reason for not renewing my passport is simple. To safe time and money. The Dutch government makes it very hard to renew your passport and there are only few places in the US where you can go. I would have to travel for hours, and invest in a trip that probably would be unnecessary if US citizenship would give me the same travel rights.
Citizenship is in your heart, I just need Citizenship to get on with my life, and have the ability to travel. If the Dutch passport wouldn't be such an issue I would probably just renew my GC, if possible.
Thanks for responding, I really appreciate it. It makes me confident about taking steps towards citizenship.