Over here baby,
I don't know whether or not Sheikha Mowza is Hazza's cousin but they are related I think.
Hazza is the son of Baba Zayed. Sheikh Zayed bin Sulthan al-Nahyan, he is the President of the UAE and ruler of Abu Dhabi (the biggest emirate I believe and also the capital).
Mowza is the daughter of Sheikh Mohammed bin Butti
al-Hamed, he doesn't rule any emirate but he's the "head" of a tiny place named Al-Ain (Baba Zayed's either place of origin or favorite place).
Baba Zayed's mother's name was Sheikha Salamah bint Butti
. It is confusing but the al-Nahyan tree is endless.