Barbiturates are essentially fat-soluble drugs. That means they dissolve into body fat, and slowly leech out over time. So, for most barbiturates (caveat - MOST), if I were to take the drug today, I would test positive for anywhere from 1 to 4 weeks. Now, it isn't impossible for a mom who has taken a barbiturate to test negative while her baby tests positive, but it is pretty unlikely. Were I in your family, I would demand a few things:
1. Repeat test.
2. Demand a thorough inspection of the lab where the test was done. This includes all lab employees.
3. A thorough explanation from those making the accusation. How do they think mom gave the barbiturate to the fetus while managing not to absorb any of the drug herself? (Note: It is possible, however unlikely. While the placental barrier might only allow a barbiturate to slowly leech to the baby, it would likely allow an equally slow leech back out. Therefore, if there was enough in the baby to be detectable, it should also have been detectable in mom.)
4. A complete list of ALL hospital personnel, including housekeeping, maintanence, nursing, and ancillary service (respiratory, radiology) personnel who might have had unaccompanied access to my child.
5. A complete list of all medications administered to all infants in the nursery since the birth of your cousin's child.
6. A complete list of all medications taken by all hospital personnel having access to your cousin's child.
If your cousin is absolutely sure that she took no barbiturates during her pregnancy, she absolutely should not accept these actions meekly. CONTACT A LAWYER ASAP.