Many years ago, a friend of mine was a family court judge in northeastern New Jersey. She found that a disproportionately large part of her docket was domestic violence cases from immigrant communities, in which husbands and fathers reacted with beatings to their wives and daughters behaving like American women instead of as they would have in the old country.
Bottom line is, the demand to enforce sharia law in Western countries -- or rather not to have the state interfere with its enforcement by private groups -- is a demand that the civil law not interfere in the power that Muslim men exercise over what they are pleased to regard as "their" women. Much of the supposed Muslim grievance against European values is that Muslim women, who see the freedom available to them in Western countries, refuse to submit, and the secular state offers them the same protection against male coercion and violence that it offers to any woman.
It is outrageous to suggest that because of her religion a resident of the UK should forfeit the protection the law offers to all women with respect to marriage, divorce, child custody and maintenance.