First you have to determine whether the kids are actually your dependents or not. If they are your dependents, you can choose not to claim them, but that doesn't change the fact that they are your dependents. They most likely are your dependents, but you can use the tool at the following link on the IRS web site to make sure.
Whom May I Claim as a Dependent?
What is the exact reject code and message that you got? Removing the kids as dependents might not be the way to resolve the reject.
Did the kids file their own tax returns? If so, they might not have indicated that they can be claimed as dependents. If that's what they did, and you can claim them, they have to file amended returns showing that they can be claimed. Note that it doesn't matter whether you actually claim them or not. They must indicate that they can be claimed as dependents. If they did not indicate that, then you will not be able to e-file your tax return claiming them, even after they file amended returns.
It's unlikely that there would be any benefit from your not claiming them. You cannot claim the education credit for their educational expenses if you do not claim them as dependents. You didn't say what errors you got in the review when you removed them as dependents, but it might be that you are still trying to claim the education credit.
