Legal Question in Family Law in Virginia

No, you've been obviously misinformed; your cousin could never be ordered by a court to pay for the lawyer's kids for which he (your cousin) would have no legal responsibility.

What may be happening is that a Virginia court, when setting child support, can look at the support obligations of a parent toward other children of that parent; for example, your cousin's former wife now has two other children to help support and that can be brought into the calculation of child support.