Praise be to Allah.
If you are travelling to visit your father, then you decide to do ‘Umrah, there is no stipulation requiring you to stay in ad-Dammaam for three days; rather you can go for ‘Umrah whenever you want, and enter ihram from the miqaat from which the people of ad-Dammaam enter ihram, which is Qarn al-Manaazil (as-Sayl al-Kabeer), near at-Taa’if.
The basic principle is that whoever comes wanting to do ‘Umrah must enter ihram from the miqaat, and the miqaat of the people of Egypt is al-Juhfah or Raabigh. But if a person is going to go to another city, such as al-Madinah, Riyadh or ad-Dammaam, it is permissible for him to delay ihram, then enter ihram from the miqaat of the people of the city that he goes to. Please see the answer to question no. 96758.
And Allah knows best.