Her full name is: Azza bint Nayef Abdulaziz Ahmed al-Sudairi.
Given the prominence of the family, I wouldn't be surprised if the bride's mother is indeed somehow related to Hussa bint Ahmed al-Sudairi (the mother of the famous 7 (and one more son and 4 daughters)). Of course there are many Ahmeds, but it seems both Azza's paternal great-grandfather is called Ahmed al-Sudairi as well as the grandfather of the Sudairi seven. So, if we are talking about the same Ahmed, the bride to be would be a cousin twice removed from the current king.
Rajwa - Azza - Nayef - Abdulaziz - Ahmed
Salman -
Hussa - Ahmed
Edit: According to
wikipedia Hussa does indeed have a brother called Abdulaziz (again not an uncommon name - also shared by her own husband); but theoretically it is still possible that we are talking about the same Ahmed Al-Sudairi.
Both the Al Saif family as well as the Al Sudairi's are prominent in the Najd region where the Al Saifs are sheiks of the town of Al-Attar in Sudair, Najd and the Al Sudairi's are part of the noble Dawasir tribe settled in Al Ghat, Najd - about 100 km further down the road from Riyadh.