The first Thunderbirds show was in 1953 flying the F-86G Thunderjet, the Thunderbirds never flew P-47's. Your relatives were picked because of the time they spent flying with the Sky Blazers in Europe in the late '40s flying P-80Bs. On a side note, your relatives also didn't fly the P-47s as both flew P-51s during the war with the 8th AF's 352nd Fighter Group and then P-80s after the war with the 36th Wing.
It's cool that you have such relatives in your family tree but not to be mean or anything but I think it's safe to say that the only 'gene' you inherited from them was a love of aviation.
ack-ack