 Solution

Conditional on both generation-2 siblings carrying the specified copy $q$, each passes it to each of their three children with probability $1/2$. Their outside partners do not carry that ancestral copy. There are six independent meioses, one for each generation-3 individual forming the three cousin marriages. ConsequentlyThis calculation ignores phenotype ascertainment in a genetic study, as requested; conditioning on the later disease observations would force these transmissions rather than assign them their prior probabilities.