Now this has not been my experience, it has been for a couple of my friends, because my ex husband and I parted rather amicably. In Islamic law, apparently a man amicably divorcing a woman is easier. A woman going to the Islamic authority is way harder.
In Canada, all of my Sunni girlfriends going to petition for divorce, were turned down by many many authorities. ...Even if their husbands were despicable losers, and they had definite grounds to divorce theirs a**es. Like, a guy is emotionally abusive to her, or physically abusive, or he married another wife but supported them unequally financially (like, left one to live off the charity of others in a war zone etc.).
So, after trying in Canada, what does she do? She comes to Oman, that's what she does.
She goes to the local court, which in Muscat was the Al khoud or Seeb one I think. Having an Omani translator helps those who cannot speak Arabic and don't know where to go.
If her husband is not Omani and she's not Omani, well then, the Islamic courts here treat her pretty fair under Islamic law. They ask her to state what grounds she is suing for divorce (like, "my husband is an alcoholic man-whore" or something). Then, they send her (usually Khaleeji) husband a summons to defend his case). If he doesn't show, they grant her the divorce. If he does show, he has to prove her wrong. Which in, any of the cases that I have seen, he couldn't.
...The process was faster for the girls who didn't want money from the loser, even if he still owed them their maher/dowry or something.
For custody of children, the courts did find the mother to be the more responsible parent, for the man was either abusive, or financially negligent, or a bad practicing muslim etc. Have no idea how custody would go however, for a woman suing for divorce on only "I'm not happy with him and can never be so" grounds, however. The father might get the kids then.
Thought that might be useful to some Muslim girls.