Catherine was daughter of Czech King George of Poděbrady and wife of Hungarian King Matthias Corvinus, who died in childbirth in 1464. Lets assume she survived and her son too.
What is going to happen then?
Matthias and George were allied at the time, but eventually Matthias turned against his former father-in-law. George went into conflict with the Pope and started to look for Polish support (Casimir IV of Poland also had problems with Papacy because of his conflict with Teutonic Order) and promised to make Casimir's son his successor. But relations between George and Matthias should not deteriorate that much if Catherine lives. George would want to see him as his successor in such scenario and thus Matthias would not turn against him.
Hungary and Bohemia were also claimed by Habsburgs and Jagiellons, so if Matthias holds bot thrones, it should improve relations between HRE Frederick III and Casimir IV of Poland, as Matthias is their common enemy (he was also IOTL, but things were complicated by the fact, that Vladislaus Jagiellon was elected as Czech King, but Habsburgs refused to regognise his title and even ignored him during Imperial election). But while Matthias would have the Emperor against him, he'd still have good relations with the Pope, because Papacy viewed Hungary as shield against Ottoman expansion into Christian lands. And considering the fact, that even IOTL Matthias was able to humiliate Habsburgs, taking Vienna from them, Frederick III is not going to have easy life (especially with Matthias less concerned about succession, as he'd have legitimate adult son).
What is going to happen then?
Matthias and George were allied at the time, but eventually Matthias turned against his former father-in-law. George went into conflict with the Pope and started to look for Polish support (Casimir IV of Poland also had problems with Papacy because of his conflict with Teutonic Order) and promised to make Casimir's son his successor. But relations between George and Matthias should not deteriorate that much if Catherine lives. George would want to see him as his successor in such scenario and thus Matthias would not turn against him.
Hungary and Bohemia were also claimed by Habsburgs and Jagiellons, so if Matthias holds bot thrones, it should improve relations between HRE Frederick III and Casimir IV of Poland, as Matthias is their common enemy (he was also IOTL, but things were complicated by the fact, that Vladislaus Jagiellon was elected as Czech King, but Habsburgs refused to regognise his title and even ignored him during Imperial election). But while Matthias would have the Emperor against him, he'd still have good relations with the Pope, because Papacy viewed Hungary as shield against Ottoman expansion into Christian lands. And considering the fact, that even IOTL Matthias was able to humiliate Habsburgs, taking Vienna from them, Frederick III is not going to have easy life (especially with Matthias less concerned about succession, as he'd have legitimate adult son).