I claimed my two dependents this year and my ex husband was to claim them. How do I get this resolved to where he can come them and they reject on my end?

If you already filed and claimed the children, and your return was accepted,  then you will need to amend your return after it has been fully processed by the IRS.   The other parent who can claim them will have to file by mail.  By using their SSN's you have blocked anyone from e-filing using the children's SSN's on a return for this year.   Waiting for you to amend will not help them.   He can mail his return whenever he has it ready.   

What is not clear----who was the custodial parent?  Who did the children live with?   Who did they spend the most nights with in 2023?   The IRS cares about physical custody.   Is there a signed agreement between you and the other parent?    Is there a signed form 8332?

If I understand correctly you claimed the children but he was supposed to. I am going to assume that the children live with you. In that case you have to amend your return to list your children on your return but check the box saying that you are not claiming them. That way you can still file as Head of Household and claim EIC and child care credit if otherwise qualified. You give your ex a signed form 8332 giving him the right to claim the children and receive child tax credit. He will have to mail his return with an explanation that you are amending yours to allow him to claim the dependents. Amended returns take 3-4 months to process.