I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
You have the ability to file a Notice of Intent to Relocate with the court that entered the original custody order. The court will send a copy of the notice to the father, and then the father can request a hearing or the judge will schedule on on his own. Because it's not possible to do shared custody between Ohio and Texas (especially with school-aged children), the judge will probably decide to do a hearing. Here is a sample notice. You may want to call the family court in your county to see if they have a specific form they want you to use.
If the father will sign the Notice of Intent to Relocate with you, stating that you're both planning to move, then the judge will probably decide a hearing is not necessary. So it might help to ask him to sign something. Ohio Rev. Code, Section 3109.051(G) does require that you give the court notice, even when the other parent agrees. Hopefully, since he's already agreed to move, he won't mind signing the notice.
If he won't sign, then you're required to also file a Motion for Permission to Relocate, showing the judge why it's in the children's best interests to move to Texas. The request should focus on the children - the importance of spending time with their grandparents, their relationship with you versus their relationship with the father. If your new job or a lower standard of living where you're going will help you give the children a better life, that is something to mention. Things like that. Here is more information:
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