Hi fandesacs,
Sharia law dictates that a non-Muslim may not inherit from a Muslim and that the legitimate child of a Muslim father is automatically a Muslim. However, there would have been no restriction on Mahra's father giving her non-inheritance monies. Additionally, since she was raised into her teens as a Christian, she could not be compelled against her will to convert unless she was willing. I believe she was probably told that conversion was a prerequisite to going public as an official member of the family. It seems easy when you're 16, but sharia is a complex legal system that impacts every part of life for the Muslim. Jews, who also have an involved system of law, actually discourage conversion to Judaism for this reason.
The only thing I disagree with you about a little is what she expected from her new family. I would be willing to bet that she did not understand the family dynamics of her new clan. Out of two dozen siblings, I'm sure she expected to find a few friends and allies. She appears to be her mother's only child and maybe she longed for a big family.
What she is doing now by openly dating is probably what her siblings feared from the minute they found out about her: a Western-reared sister who might dishonor the family reputation. So they carefully distanced themselves from her. Ironically, by isolating her they may have actually caused her to return to Europe and find a boyfriend and social life outside of Emirati cultural strictures.