He's widower with two surviving female children (in their early teens). He's the legitime claimant to the Norwegian throne as it is inheritable, while the Danish are electable as such his uncles claimare legitime there. Denmark hasn't converted yet at this point, but Christian converted himself because of Protestantism popularity in Denmark. But let imagine he doesn't convert, because he need the Emperors support.
I read that he converted to Protestantism some time in his exile in 1520-s, but then returned to Catholicism because he needed emperor´s support, and was Catholic by his Norway expedition in 1531.
His major supporter in Norway was the Catholic archbishop of Trondheim. So they stay Catholic.
With money from the emperor he succed in gaining control of Norway but fail in Denmark. Christian and Frederik reach a agrement where they split Denmark-Norway up, Christian get Norway and Frederik Denmark, Gotland and Schleswig-Holstein.
Christian remarry and decide to marry his oldest daugther Dorothea to James V of Scotland after his wife dies.
Christian´s daughters are Dorothea, born 10th of November 1520, and Christina, born November 1521.
OTL, they married Christina in 1534 (age 12) to Francesco Sforza of Milan, and Dorothea in 1535 (age 14) to Frederick of Pfalz.
Christian II-s victory in Norway is a PoD in 1532 which butterflies these marriages away because his daughters are now more attractive heiresses.
James V was an eligible bachelor at the time. He was finally married age 24, on 1st of January 1537, to Madeleine of Valois.
Could we butterfly this away, so that James marries Dorothea of Norway in the first place, in 1536?
Any comments about the politics of the marriage negotations? How would Henry VIII react to Scotland allying with Norway, and thereby also Spain, rather than France as per OTL?
But while James get two sons with Dorethea, Christians doesn't get any male children. With James early death Dorethea become regent for her eldest son until he reach majority, she keep a close relationship with her father. Her father death result in her eldest son inheriate Norway, which are the beginning of the Scottish-Norwegian Union.