"I didn't get the$1500".
The other reply assumes you are asking about the Economic Impact Payment (EIP), also known as the Stimulus payment. The other answer is correct, cousins, even 1st cousins, are not qualified children for the EIP.
My answer assumes you are asking why you didn't get the $500 (per dependent) credit for other dependents, on your tax return.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). Her children are not related closely enough to be QCs and they did not live with you long enough to be Qualifying Relatives ("stayed with me part of the year"). A cousin needs to live with you all year, to be a standard dependent.
If she had any earned income at all, it may be best if she claimed them, or better yet, let the other parent claim them. They are worth up to $2000 each to the non-custodial parent.
