All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no doubt that such actions on the part of your father, if proven true, are odd. It is strange that he would threaten not to speak to you if you do not pay the rent or to cause you problems because of it and the like of such behavior.
However, you should bear in mind that he is still your father, and you are enjoined to show dutifulness and kindness towards him. We believe that you already know that; please refer to fataawa 82254 and 87019 on the virtues of dutifulness and kindness towards parents; so try to meet his request as much as you are able to and earn his pleasure, especially if this would not cause any harm on you. You did well by keeping your relationship with him safe from the causes of discord.
It has been narrated on the authority of Jaabir ibn ‘Abdillaah that a man said, "O Messenger of Allaah, I have wealth and children, and my father wants to take my wealth." He, sallallaahu ‘alayhi wa sallam, said, "You and your wealth belong to your father." [Ibn Maajah]
The general indication of the hadeeth means that the father has a right in his child's wealth. However, scholars underlined that there should be limits and conditions to the father's entitlement to his children's wealth in order to preserve the best interests of the children. Ibn Qudaamah wrote, "The father is entitled to take whatever he wishes from his children's wealth, regardless of the father's need or the child's age, provided that two conditions are met. Firstly, the father must not wrong the child by taking all his wealth, causing harm to him, or taking what his child needs. Secondly, he must not take the wealth of one child to give it to his other child..." [Al-Mughni]
For more benefit, please refer to fatwa 89942.
We hope that you would not regret paying money to your father and strive to offer him the money willingly with a good heart; you will hopefully reap the fruits of this righteous act in the worldly life and the Hereafter.
Allaah knows best.