I negotiated with my ex-husband that the children would immigrate with me, and he refused to sign the documents.

When you decide to emigrate, if you have an argument with your ex-husband about the custody of your child, you'd better take the following steps:

1. consult a professional lawyer: consult an immigration lawyer or a family lawyer, who can provide specific legal advice and guidance.

2. Communication and negotiation: Continue to communicate and negotiate with the ex-husband to find knowledge or solutions. You can try to reach an understanding through friendly discussion, or seek the assistance of a third party, such as a family counselor or mediator.

3. Submit an application: If the ex-husband does not agree to sign the document, he can submit an application to the court for a ruling. In this process, you need to provide relevant evidence and reasons to support your application.

4. Consider litigation: If the problem cannot be solved through negotiation or mediation, consider filing a lawsuit. Please consult a professional lawyer to understand the proceedings and possible results.

Please remember that each situation has its own uniqueness, and the above suggestions are for reference only. You'd better consult a professional lawyer before taking any action.