WI the House of Barcelona doesn't die out (Peter of Aragon lives) ?

Martin I of Aragon, the last king of the House of Barcelona, died in 1410 without surviving legitimate heirs, as his son Martin I of Sicily had died less than an year before. It caused a two years interregnum, when six candidates competed for the throne. Eventually, Ferdinand of Trastamara, a Castilian prince, was chosen as monarch.

However, Martin I of Sicily had a son that died in a freak accident: the young prince Peter, born in 1398, was only 2 years old when he was killed by a spear in the head during a tournament.

So, WI the accident never happened and Peter lived to succeed his father in Sicily and his grandfather in Aragon? What could be the consequences of a continuing House of Barcelona in both kingdoms?

Possibly no union of Castile and Aragon, stronger Aragon as a Mediterranean kingdom, and possibly an Aragon that would be a true rival to Castile. Stronger ties between Sicily and Aragon for sure. If de Barcelona survives into the late 15th/early 16th century, it would be interesting to see the consequences of that.

Draeger said:

Possibly no union of Castile and Aragon, stronger Aragon as a Mediterranean kingdom, and possibly an Aragon that would be a true rival to Castile. Stronger ties between Sicily and Aragon for sure. If de Barcelona survives into the late 15th/early 16th century, it would be interesting to see the consequences of that.

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This is after the black death, so Castile still has the weight of numbers on her side. Add this to the wealth of the new world, and Aragon still likely ends up in Castile's orbit. Whether or not she later has the strength to break away ala Portugal is another question.

I'd expect the Castilan/French alliance to live on, against an Aragon continuously seen as the main Mediterranean rival of France and Castile.

Maybe it could mean a stronger royal authority, above the assemblies not needed to resolve this conflict (it's always a bad idea asking them to decide who would be king), a lesser Castillan influence on the peninsula.

It could help limiting bandositas, but Peter IV's costly reign made hard avoiding them entierly.

Geopolitically, it could change things for Castile :you won't have a common geopolitics, but probably similar interests on what remains of Al-Andalus and North Africa. It could divert a bit Castile from Atlantic matters, at least partially.
Not that Castile would be deprived of a strong naval side, of course, by this time it was already a naval power, but it would be more rivaled.

because the Aztecs at first believed them gods and weren't prepared to defend themselves as well

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While agreeing to the general point, this was much "interpreted" by Conquistadors at their benefit. Aztecs may most probably having been less naive.
What played more than technology or "luck" (which is another name for "factors we don't know about") is the help that conquistadores recieved from local peoples, opposed to Mexicas.

One shoudn't forget about the conquistador mindset, that was in the same line than the end of Reconquista; with the desire for new lands (more than gold itself) being lumped with a religious drive. ITTL, without Castile/Aragon being together on Nasrid Grenada, it may be develloped differently.

France, England and even less Scotland have a real chance to get in Mesoamerica first (having other geopolitical focus, and maybe simply not enough ressources to do that in addition) but even if Castile comes there first as IOTL, a full-fledged conquest of the region isn't bound to happen.

Although giving the ineluctable epidemic shock, military technological advance, and geopolitical situation; I'd expect a coastal takeover with at least a strong vassalisation/clientelisation of the hinterland.

Just some more ideas:

a) if Peter lives, securing the thrones of Aragon, Sicily and Sardinia, what would happen to Fernando of Trastamara now that he doesn't become king?

b) with the young prince alive, could his mother Mary of Sicily also live? If so, Blanche of Navarre wouldn't marry Peter's father Martin. So, who could be a possible candidate for her hand? Also, it could affect the marriage or her sister Joanna as well (she was intended for Martin at first, but he ended marrying Blanche).