Thats a very good question.
And if we take the question in the opposite side? They have this freedom... simply because they consider they are entitled to.. and they would not accept to be different ?
Let"s take case per case.
Princess Haya, daughter of King and sister of à ruling King, descendant from Profhete ...Raised in England, like the purest Bristish aristocracy... already well known internationally, used to a free life (she proved it....)
Would she accept to put the Hijab and disappear on purdha? For me No. And she didn't... if Sh. Mo took advantage of this... to think about, but in any case I doubt he had choice.
Sheikha Mahra for me is a more complicated case. You have a girl raised in an occidental country, used to live like an occidental girl. And suddenly in her hot teenage age (17 or 18) she finds herself in a completely different country, she needs to adapt. For some years her way of llife I would say hurts... and her main occupation is related to horses. Then she disappeared..one thought was that she could not adapt to life there. And she appeared again, with a completely different appearance and with her main occupation : invitee in official public events. Orientally dressed; then marriage with a local and motherhood. Before her marriage she spent a decade with no private life (unless fully hidden). For someone raised in Europe, this decade 18-28 is the top of age to live her private life. If she did...she did it well secretly.
So here also we have a scenario, not of a granted freedom ... but a reduced one.. what an Emirati eye sees as a high freedom...is the opposite. She could not oppress more... she did a lot.
Could her father ask her more? Apparently not (we don't know if he wishes to...)
And here we have also a strange behavior. The same man who kidnapped 2 daughters.. and emprisonned her for ever.. he has another daughter, left to be raised abroad, as a Christian European teenager, without issue. It is unclear if he was aware about her existance since day 0, but for sure when she was a kid, he was present in her life.
Why he didn't ask to bring her in Dubai ? Mystery. He could have kidnapped her ... in 5 minutes. Nut he didn't. He kept her other kids away from her mothers (Manal's mother) he gave Latifa 2 to be raised by another woman... but here.. freedom..
Maybe his behavior is different depending on the mother?
Food for thought