Can she be held responsible for his travel expenses to visit his daughter or can he deduct that from child support?

Ex-wife does not have the right to create obstacles to visitation. However, ex-wife can't be held responsible for your boyfriend's travel expenses related to visitation, & he can't deduct same from child support. It was not a good idea for your boyfriend to just agree to the move without considering his visitation situation. A skilled family law attorney, like me, would need to discuss this matter w/your boyfriend in greater detail, & ask him many questions, in order to give him the complete, proper legal advice he needs, & a quote to represent him.? He should schedule a consultation ASAP. Once the matter is resolved to his satisfaction, he'll be glad he paid the money to hire an experienced attorney & properly protect his, & his daughter's, legal rights.