I think that the objections of “adocs” and “147” are non-starters. The Tefilla for Agunos was written for a unique tragic situation: women who cannot remarry because they are denied the Halachic “bill of right” to do so by a husband who uses the Torah’s laws to hurt her. The case where a husband is denied parenting rights is truly an inexcusable injustice perpretrated on him and on the children by the wife, but is not anywhere in the same class of tragedies as the Agunah case is. To criticize a prayer for an Agunah because it is not “gender neutral” is like critizing a Tefilla for sick people because it did not include other groups of suffers such as financially impoverished people.
The Agunah’s tragedy is precisely because the Torah’s laws are being “hijacked” (I borrowed this phrase from George W. Bush) to punish the woman (i.e. deny her the right to remarry) by the husband for his selfish reasons. The case where a wife is being unreasonable and unfair to her ex-husband, has nothing to do with “hijacking” the Torah’s laws.
No man has the right to use his Torah-itic powers over Kiddushin and Nissuin to deny his wife the basic right to find her true Zivug once the marriage is irrevocably over. The right for a woman to receive a Get is a so fundamentally undeniable, that it must NEVER be held hostage by financial, custodial or other negotiating positions. I have the right to say this since I am an ex-husband who was dealt painful “hard-ball” tactics by the ex-wife; yet it would be unconscionable to me to hold up the Get process even in the face of these tactics.