Can the parent of a deceased person force a woman to take a paternity test in the state of virginia

Are they applying for grandparent rights or something else through the courts?

Actually the father takes a paternity test. Pater-Latin for Father .
Genetic testing is used to determine biological parentage by comparing the DNA markers of the mother, alleged father, and child.

VA does recognize Grandparent rights (Grandparent Rights in Virginia (http://www.livesaymyers.com/grandparent-rights-virginia/)). Based on what this site says, the court will consider the best interests of the child in determining whether visitation will be granted.

However, I don't know if they will require paternity testing. If the grandparents go to the court and say they want visitation, but only if the child is biologically related, they may deny the petition. I strongly suggest contacting a local Family Law attorney who is more aware of the mood of the courts.

Of course a woman doesn't take a paternity test - she can't possibly be the child's father (unless she had a sex change operation after fathering the child). If the OP meant to say "maternity test" -- is there a question as to whether babies were switched at birth?