D.Miguel (II) Duke of Bragança, by the time he fathered his last daughter, Infanta D.Maria Adelaide (31.Jan.1912) was already the grandfather of Nada of Bragança, the duke of Viseu's eldest daughter (b. 28.June 1910).
But the case you outlined was about first cousins, once removed, which is nothing unusual. I already mentioned cases of second cousins, once removed where a person belonging to an older generation was younger.
This sort of thing typically happens when there is a large family with lots of children spaced apart, where the older children marry young and the younger children marry late. Look at Infanta Maria Josefa of Portugal (born in 1857), who married young (in 1874) and had three daughters in quick succession. The said daughters (Duchesses Sophie Adelheid, Elisabeth, and Marie Gabrielle in Bavaria) didn't marry especially young (all were in their 20's).
But they started having children from 1900 on, when their aunt Maria Ana (consort of the future Grand Duke Guillaume IV of Luxembourg) was still having children (her last child in 1902).
So Princess Sophie of Luxembourg had first cousins, once removed who were older than herself. And her sister Antonia had a stepson (Albrecht, future head of the royal house of Wittelsbach) who was only six years younger.
I was interested mainly in situations where an aunt/ uncle (or half-aunt/half-uncle) was younger.
Princess Stéphanie of Belgium, Crown Princess of Austria, Countess Lonyay, had four grandchildren, Prince Franz Joseph zu Windisch-Graetz in 1904, Prince Otto Weriand in 1905, Prince Rudolf in 1907 and Princess Stephanie in 1909, when her sister Princess Clémentine of Belgium married Prince Victor Napoléon in 1910, followed by her two children Princess Marie-Clotilde in 1912 and Prince Louis in 1914.