It does not matter at all what your children want. The question that they have to answer on their tax returns is "can you be claimed" the question is NOT "are you being claimed". So, whether you actually claim them or not, they have to answer that they can be claimed. If you don't actually claim them, then you will lose their personal exemption of $4,050 each and you will pay tax on $9,100 more income than you would otherwise have.
