I changed my mind ...

For either child, that child could be

G) a girl (1/2)

BT) a boy born on Tuesday (1/2 * 1/7 = 1/14)

BN) a boy born NOT on Tuesday (1/2 * 6/7 = 6/14)

If we reguire exactly one child is (BT), the options are

(BT)*(BN) = 6/196

(BN)*(BT) = 6/196

(BT)*(G) = 1/14 = 14/196

(G)(*BT) = 1/14 = 14/196

where the order listed is the birth order.

These are all the families that have exactly one BT. So if we looked at 196 families, there would be 6+6+14+14 = 40 with one BT. Of these 40 families, 12 have 2 boys = 12/40 = 3/10 = 30%

If you include (BT)(BT) with two boys born on Tuesday, there is one more out of 196. So there are 41 possible families, of which 13 have at least 1 BT. Which is 13/41 = 31.7%