Education

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.

Your  kids erroneously did not check the box, on the their form 1040, saying they can be claimed as a dependent.  You can no longer e-file.  You have to mail in a paper return.  You can and should claim them as dependents*.  You should also claim the education credit on both students.

They will have to file amended returns, unclaiming themselves. You do not have to wait for them to do that.  You can paper file now. 

*This assumes they qualify as dependents. There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on him self.

Furthermore, there is a rule that says IF somebody else CAN claim him as a dependent, he is not allowed to claim himself. If he has sufficient income (usually more than $12,550), he can & should still file taxes. In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.  TT will check that box on form 1040.

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

They both made over $3900 last year so need to file on their own.

For an undergraduate college student that was under the age of 24 on Dec 31 of the tax y ear, their earnings do not matter. They could earn a million dollars and still qualify as your dependents.

Even if they are required to file their own tax return, that does not prevent them from qualifying as your dependent, and does not prevent you from claiming them as your dependent.

If the student is required to file a tax return and qualifies as your dependent, then the student must select the option for "I can be claimed on someone else's tax return".  Note that it does not matter if you actually claim them as your dependent or not. The key word is "QUALIFY". If you the parent qualify to claim the student as a depdendent, and that student is required to file a tax return, then the student must select the option to indicate they can be claimed on someone else's tax return.