They seem to have had a pretty good relationship when the princesses were children with very long odds of coming to the throne. James didn't like being geographically separated from them, such as when Anne went to the French court as a young child to deal with an eye disorder of some kind, so it was good that he was only Duke of York at that time - a king's children were usually raised in their own household, often away from court. However, at least Anne seemed to be somewhat afraid of him, claiming when he asked for her thoughts later in life that she wouldn't talk about important issues with him in case he became angry. In general, she was a very quiet child and teenager, saying of herself, "I have not, maybe, so good a way of expressing myself as some people have" (though she considered herself to at least have sincere feelings when she did express them).

James did hope for a conversion from his family members, particularly once his first wife, the princesses' mother, converted to Catholicism at his urging a few years before her death. It was truly unlikely, though, given that the atmosphere in Restoration England was extremely anti-Catholic and that the reaction to the Duchess of York's conversion, when it became known, was extremely negative in the family and in the court. But Mary and Anne were raised Protestant at the order of the king, under the instruction of Henry Compton, the Bishop of London and a militant Anglican, so there was very little chance that he would be able to convince them. Mary in particular studied up after her marriage in order to argue against their father when he sent her Catholic tracts. Anne did hate Catholicism as well as Catholics in general, but she didn't seem to hate her father for his religion.

The father-daughter(s) relationship certainly must have deteriorated somewhat when James remarried, because the princesses disliked their stepmother, Maria Beatrice of Modena - not entirely unrelated to that anti-Catholic atmosphere and upbringing. By 1688, when the queen was pregnant with the fetus that would become the Old Pretender, Anne was speculating in her letters to Mary that she thought the queen's belly was fake; however, she had pleasant chats with her father at the same time in which she never mentioned that she agreed with these rumors, which he thought were ridiculous. He also encouraged her to go to Bath shortly before the birth was expected (instead of waiting to attend on the queen and witness it, as he'd planned) because her physicians said that it was necessary.

But by the end of July 1688, Anne and her husband had committed to the plan for William of Orange to invade, though she kept it quiet, and once he had deposed her father was seems to have been terrified of facing him. Until sometime later he assumed that his daughters had known nothing, and even when he found that Anne did have a hand in it, his response was to blame the Duke of Marlborough for "corrupt[ing his] child". Several years later, he was still speaking of her kindly while apparently giving up on Mary; Anne would write to him seeking forgiveness (potentially as a way to get herself declared his heir, at a time when William and Mary could still be seen as temporary regents), a move that turned just about everyone but her father's partisans against her, and in 1692, when he attempted a re-invasion, there was an attempt make to get her to help him back to his throne.