Praise be to Allah.
Doing ‘umrah repeatedly in a single trip is not the practice of the Prophet (blessings and peace of Allah be upon him) or of his companions, therefore it is makrooh, as has been explained previously in the answer to question no. 111501
But seeing that you made a vow to do ‘umrah on behalf of your father, your paternal uncle and your maternal uncle, and you are coming for ‘umrah from Egypt, there is nothing wrong with you fulfilling your vow in a single journey, because you may not be able to travel to Makkah a number of times. So if you want to do ‘umrah whilst you are in Makkah, you can go out to at-Tan‘eem or some other place beyond the Haram boundary, then enter ihram for ‘umrah.
You should understand that making vows is makrooh and does not bring anything good, as the Prophet (blessings and peace of Allah be upon him) said. Al-Bukhaari (6608) and Muslim (1639) narrated that Ibn ‘Umar (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) told people not to make vows and said: “They do not avert anything; all they do is get something out of the miser.”
And al-Bukhaari (6609) narrated from Abu Hurayrah (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him), that Allah, may He be exalted, said in the hadith qudsi: “A vow does not bring the son of Adam anything that I have not already decreed; rather what reaches him is determined by the divine decree, and that has already been decided. But (the vow is only) to get something out of the miser.”
Although vows are makrooh and disapproved of in principle, whoever makes a vow to do an act of obedience to Allah is obliged to fulfil it, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever vows to do an act of obedience to Allah, let him do that act of obedience to Him.” Narrated by al-Bukhaari (6202).
We ask Allah, may He be exalted, to grant you relief and a way out from all difficulty.
And Allah knows best.