How can the mother and her brother, who resides in Hail, enter into ihram, and what type of ritual (nusuk) is for them, noting that her brother will take her from Riyadh to Jeddah, then to Mecca for Umrah, and then they will remain for Hajj?

It is better for your mother and your brother to perform Hajj as mutamatti’in. They should assume ihram (definition) for 'Umrah (definition) from the miqat (definition) for the people of Najd (Al-Sail Al-Kabeer). After performing tawaf (definition) and sa'i, they should exit ihram by shortening their hair. Then, they should stay in Makkah until the Day of Tarwiyah, when they assume ihram for Hajj and perform its rituals. They will owe a sacrificial animal for tamattu’. It is also permissible for them to perform qiran (definition) by intending both Hajj and 'Umrah together from the miqat, and they do not exit ihram until after completing the rituals of Hajj. They will perform a single sa'i. However, tamattu’ is better.