Praise be to Allah.
If the situation is as you describe, then you are not being disobedient to your father by going against him when he tells you not to fast on both Monday and Thursday, because your fasting two days is an act of worship, so long as you are able to do that, and there is no obedience to any created being if it involves disobedience towards Allah. Moreover, what appears to be the case is that he is trying to be kind to you and is not forcing you not to fast.
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Mohammed and his family and companions. End quote.
Fataawa al-Lajnah ad-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Iftaa’ (25/198)
And Allah knows best.