custody rules

the case is taking place in Binghamton, NewYork. My fiance's ex-wife has legal custody of their 3 year old, although he has one night a week where he has here overnight. Even though she has custody, she requires him to pick her up every morning to take her to day care and to pick her up in the afternoon from daycare. He has her until 7pm and then takes her home. She also requires him to come over when the child has a bad dream or has trouble sleeping. He does all the doctor visits, has her for almost every holiday, etc. If he says no to any of her requests, she lays the guilt trip on, calling him a "bad" parent and irresponsible. She very recently got married, within the past week, as is also 4 months pregnant. What can he do? He has only recently called for legal advice, but fears he may not have any recourse to control her. They also, unfortunately, used the same lawyer for their divorce and used mental cruelty for the reason. It was really for adultery on her part, 3 time!