You have some of it right, and yes, it sucks (spent 3 years as a "Misarevet Gat", a woman whose ex wouldn't give her an official divorce). But it goes both ways: a woman can also refuse to give her husband a divorce. In Israel, the rabbis control family law--only they can make an official marriage, and only they can give an official divorce. However, a man cannot marry more than one woman: to get remarried, he has to give a gat to his first wife. But I know a woman who's waited 20-some years for her gat, and her husband moved to Australia and is living with a woman, so it's almost the same. What happens is this: a couple goes to the rabbis and asks for a divorce. The rabbi asks each if they agree. If one refuses, the other is offered "Shalom Bait" (Peaceful Home). That means they live together as man and wife for one month, and must have sexual relations during that time. If the one who asked for the divorce still wants it after that time, the rabbi must grant it. However, for women who want a divorce, Shalom Bait is like "sactioned rape" so they often refuse it. For others, they want to leave an abusive relationship, and taking that option could be dangerous, even deadly. So they prefer to get another date with the rabbi, in a few months time, and try again. Outside of the rabbis, you can get a civil divorce agreement, which is not official, but it details alimony and custody and such. So for some women, waiting for the official divorce is no big deal, because all the important details are settled. And if he still won't give it and she wants to remarry, there are ways to get it. If he doesn't pay child support, he can be imprisoned. And sometimes, if he won't give a gat, under special circumstances, he can be imprisoned. Hauled out once a month and asked again if he will give the gat. Not pleasant, but it has happened in some cases. Anyway, this is the law for all Israel. So now some secular couples have a wedding party, without a rabbi, and never get officiallly married; they just don't want the rabbis interfering in their lives. Some couples take the Shalom Bait, and it works for them. The government can't do anything about it. Yet. There are people who are trying to get civil marriages legalized, which would mean also civil divorces; but it's a long haul. The religious minority in the govt uses its power carefully, selling their votes to others, with conditions that they get their laws passed. Like El Al can't fly on Shabbat, which costs the company and the country billions of lost custom; and so it is with ancient divorce laws.
There is a web site that explains the problems this can cause for women who can't afford to keep themselves and their children, if they can't get child support with out a divorce. You see, you open a case for divorce either in the civil court or the rabinut (rabbis court); usually it's a race between the couple: the woman wants the civil agreement, the man wants the rabbis to decide. If the man wins and they go through the rabbis, they can say there will be no child support until there is a gat. On the other hand, there are some ways to get it...if the woman opens the case first, in the civil court, she can ask for alimony for herself (not child support), which is rare in Israel, and it is to be paid until he gives the gat. And on the other hand, the laws are very much against fathers--there is no joint custody, as americans know it. Fathers almost always get every other weekend and one afternoon a week, alternating holidays. And if there's any problem at all, even if there are no grounds, the father almost always gets the short stick, even losing custody completely, while still having by law to pay child support.
I assume you're anti women's rights. Doesn't she have the right to be the parent with limited visitation rights? Are you sexist? By the way, if he files for custody and ask for a jury trial, which Texas is the only state that does it, you want women completely ban from the jury as they are far more likely to rule in his favor than male jurors.