United States
I am an attorney who practices in family court. Most states are "no fault" divorce states in which you can merely assert that the marriage is "irretrievably broken" as a basis for a dissolution of marriage. Now, if the other partner answers the petition in writing to the court denying that the marriage is "irretrievably broken" the court may require the parties to undergo some marriage counseling to determine if the marriage can be reconciled before granting the divorce. However, judges will not force parties to stay married if the petitioning spouse still wants to dissolve the marriage.
UK
If you apply for divorce and your spouse refutes it, most Judges accept your application irregardless of your spouse's response on the logic that if one person wants a divorce then the marriage is over.
Yes, most states have no fault divorce available and no longer require specific grounds for divorce. A party need only provide a general reason for the divorce such as irreconcilable differences or an irreparable breakdown of the marriage.In the US, one spouse cannot prevent a divorce.
No. Most states, including New York, have no fault divorce available and no longer require specific grounds for divorce. A party need only provide a general reason for the divorce such as irreconcilable differences or an irreparable breakdown of the marriage. No fault divorce became available in NY in 2010.In the US, one spouse cannot prevent a divorce.Can_your_husband_divorce_you_with_no_grounds_for_divorce
She will have to abide by the divorce decree and custody orders of the state in which the divorce was granted. She can move back, but the ex-husband (and the children's father) may dispute being separated from his children and take you to court to prevent it.
You can't. You can only prevent any children from being moved.
Vetoing
It is not you place to prevent others doing as they wish. Certainly not as a 'Christian believer'.
You continue with the divorce proceeding. A spouse who refuses to sign the divorce papers can delay the proceedings by making it take longer but they cannot prevent the divorce.
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If both parties will not sign the divorce papers then the court will deciede. Depends what state you are in. Indiana is a no fault state meaning if you want to divorce you will be allowed to regardless if the other party wants to or not.
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Divorce and domestic violence are separate issues. Not signing the divorce papers may not prevent the wife from getting the divorce and won't change any of the orders of the divorce such as property distribution, child support, etc.
It is the court - not the wife (or husband) who grants the divorce. In most states, if one spouse files for a divorce, the court will grant the divorce (assuming there are no jurisdictional issues). She may not want a divorce, she may not agree to a divorce, but she cannot prevent you from obtaining a divorce.