All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Similar to Hajj, every Muslim is obliged to perform Umrah once in a lifetime. Al-Shribini says (What means): "Performing Hajj is obligatory (Fard), and so is performing Umrah, according to the reliable opinion of the Shafie school of thought" The evidence on this is that Allah, The most Exalted Says, (What means):" Perform the pilgrimage and the visit (to Makka) for Allah.) [Al-Baqarah/196]. Moreover, the conditions that make performing Umrah and Hajj obligatory are the same. One of the conditions, concerning Umrah, is being responsible and able for Allah, The most Exalted, Says, (What means):" And pilgrimage to the House is a duty unto Allah for mankind, for him who can find a way thither." {Al-Imran/97}.
The ability to perform Umrah is measured by one`s financial and physical status or the financial status alone. Since your father (Questioner`s) is financially and physically unable, then his performing Umrah isn't obligatory and his sons aren't obliged to seek someone to perform Umrah on his behalf. In conclusion, since the mercy of Allah is limitless, one is at liberty to do any of the good deeds and be rewarded for that. And Allah, The Almighty Knows Best.