I want to become a monk in the Theravada tradition and have already obtained permission from my mother. My father does not live with us and never has, so according to the following passage from the Vinaya Atthakathā, I shouldn't need his permission:
A father, not concerned for the welfare of his wife and son, runs away. The mother gives her son to some monks, saying, “Let him go forth.” When asked, “Where has his father gone?” she replies, “He has run away to disport himself.” — It is suitable for him [the son] to be given the going forth.
However, I am still not sure since in his case it isn't that simple. Although my dad moved to another country, he continued to fully financially support us in the first years of my life and paid for all my school costs up to 12th grade. As far as I know, he initially had the intention to bring us over to live with him, but it seems my mom refused. Even then, he continues to visit me every year or so, and we talk on the phone quite often. One could argue that he did, in a sense, leave me, since he could have well come back and at least live closer to me, even if he had split with my mom, but I still have mixed feelings.
The reason I ask is that I know he will not agree with my ordination, since he's quite focused on money and material things, and expects me to become accomplished in those areas. He is also quite unskillful in his behavior and conducts himself pretty much opposite to the Noble Eightfold Path.