Can an individual who is the qualifying child of a tax payer be a qualfying relative of another tax payer?

Can a qualfying child who is a taxpayer qualifying child be another tax payer qualfying relative

Not sure what you are asking, so I will cover several scenarios.

You can be a taxpayer and be a dependent of someone else if you choose NOT to claim your own exemption. This is often the case with high school and college students who have summer and/or part-time jobs. Their income is so low that their $3,200 personal exemption is not needed for them to get all of their withheld income taxes refunded, so they allow their parents to claim them on their tax returns. Even if the exemption would make a difference in the amount of the refund, in most cases the exemption is worth 2-3 times more to the parents than to the child because of the parent's higher tax bracket. BTW, the final decision on this matter rests exclusively and irrevocably with the child. The parents cannot legally force the child to give up his/her exemption if the child want to claim himself/herself on his/her tax return.

In the case of a divorce, the child can be the dependent of one parent (making the parent eligible to claim the Child Tax Credit) while being considered a "qualifying person" for the custodial parent (making that parent eligible for Head of Household status and eligible for claim the Earned Income Credit).

The child CANNOT be the qualifying person for more than one taxpayer, regardless of whether that taxpayer is parent, grandparent or other relative.

If the child is a taxpayer who claims his own exemption, that child can STILL be a qualifying person for another taxpayer if the child meets all the other criteria for the qualifying person test.