Nothing against John of Gaunt, but this is low-key an England screw.
Let's start with the war effort that John II would inherit, which can best be summed up by saying that Edward III chose the
worst possible moment to die.
The most recent truce with France was set to expire in a matter of days after Edward III's death and England was on the precipice of launching a major campaign into France. The army had already been mustered and a large navy assembled to shuttle men across the Channel -- and then it had to be called off. Why? Because legally it no longer had any authority to exist. The army had been gathered in the name of Edward III and it had no right to go to war in the name of a dead man. Even if the new King John II wanted the campaign to go ahead as planned, the lords and knights who were to lead this expedition had to be on-hand to facilitate and witness the transition of power. But the men and ships had already been gathered -- and so they had to be paid. This made for an
enormous waste of money at a time when the kingdom was already cash-strapped.
But the problems don't stop there. Just as the army's authority to wage war had lapsed, so too had the diplomatic authority of Edward III's ambassadors. So, with the truce set to expire and the campaign having to be called off, the English had no ability to negotiate an extension of the truce. This gave France an open shot at invasion of English continental territories.
This above is the situation that OTL Richard II inherited, and that John will inherit in ATL. But John has one big problem abroad that Richard did not: his claim to Castile. John II would be styling himself king of England and of France
and of Castile and lord of Ireland. This union of the Plantagenet claims to France and Castile in one man very probably draws the Franco-Castilian alliance even closer together -- and makes the war even more daunting for the English.
Then, on top of this, John II has a number of domestic problems that Richard did not. Off the top of my head:
- John is a deeply unpopular figure at this point. Indeed, 1377 is probably the lowest point in John's career. He overreacted badly to the Good Parliament's reforms of royal administration, raising a small army to round up and toss a number of the reformers into jail. This was an extremely controversial move that tarred John with a wide swathe of the gentry who made up the commons -- i.e., the body that controls taxation and is now claiming new authority to oversee royal administration. This quite possibly sets up a showdown between the crown and parliament.
- The reformers of the Good Parliament came largely from the retinue of the earl of March. The counter-reformers of the Bad Parliament came largely from the retinue of Lancaster. These parliaments in 1376 and 1377 are arguably the prelude to the Wars of the Roses, as the OTL reform platform was effectively a proxy war over who was in the line of succession after Richard. (The reformers wanted to limit John's powers as Edward's de facto regent and install March in government.) This is a clear indication that March was willing to fight for his right to the crown jure uxoris, which sets him on a collision course with John in a world where Richard dies and John is recognized as heir to the throne.
- John's opposition to the Good Parliament and his actions in the Bad Parliament had made him a powerful enemy in the church, as William of Wykeham, bishop of Winchester (and therefore lord over the greatest ecclesiastical treasury in England), became caught up in the politics of these parliaments and ended up aligned against John. In OTL, Wykeham is pardoned early in Richard's reign, but who I am doubtful John would be so forgiving.
- John had made enemies in the church of England even before this feud with Wykeham, though. John's support for John Wycliffe in the 70s made him not quite a heretic, but you could say he was "heretic adjacent." One of the country's chief opponents to Lollardy was William Courtenay, bishop of London, who was a major political player both by virtue of the office he held and by his birth (his father was earl of Devon and his mother was daughter of the earl of Hereford, giving him relations throughout the peerage). Courtenay was fiercely devoted to protecting the church's interests and John's support of Wycliffe seems to have come from a belief that the church had acquired too much power in the secular world. OTL Courtenay was part of Richard's regency council and likely one of the figures instrumental in keeping John and Richard's other uncles out of power. His inability to sideline John in ATL would surely set the two up for conflict.
- Finally, John had gotten caught up in the messy politics of the London merchant scene, which -- in addition to his terrible relationship with the bishop of London -- had made him broadly unpopular with the local population. (I have to admit that I don't fully understand the messy and partisan nature of the various merchant guilds of 14th century London, but John's problems with the merchants stems from his securing a pardon for one of his tenants, John Pecche, who -- in addition to being one of John's feudal tenants -- was a corrupt fishmonger.) This is no small thing. London merchants had become powerful figures by this point in history and were an important source of crown revenue, as they routinely extended loans to Edward III to finance his campaigns. John II may not be able to tap these men for their money the way his father had or OTL Richard II's regency council did.
tl;dr: John of Gaunt has, by 1377, alienated much of the commons, has a major rival in the peerage (March), has two separate conflicts with major church leaders, and has run afoul of the wealthy merchant class in London.