You're connecting two things that are not connected.

Your client can choose to claim or not claim a dependent.

Your client's child cannot claim himself if he is a dependent of someone else.  You're a dependent based on the facts, not based on whether or not you're claimed as such.  There's a checkbox in the Standard Deduction section of the 1040 that indicates the taxpayer (child) CAN BE CLAIMED as a dependent.

https://www.irs.gov/pub/irs-dft/f1040--dft.pdf

Rick