Going out with another man, by itself, is not determinative of the custody issue, however if she constantly gets drunk around the baby, stays out late when the baby should be under her supervision, and/ or neglects the baby somehow, then that could be grounds for a modification in custody.
You would be well-served to discuss your dilemma with a New York domestic relations attorney in a confidential forum as soon as possible.
I agree with my colleague. You may be headed toward partition, but not necessarily since your cousin probably just wants to be compensated. It would be a good idea to sit down with your cousin, come up with a fair price, and retain an attorney to assist you with the buy-out.
You would be well-served to discuss your dilemma with a New York estates attorney in a confidential forum as soon as possible.
If your record is sealed, then not everybody will be able to look at your history. However, New York is not an expungement state and thus convictions do not just disappear. Here, it depends on the questions you answer on the application. Always be truthful and do not hide anything. You have been arrested, but not convicted.