Outremer
Ibelin Rule
Outremer was now dominated by the Ibelin family on the mainland. John had four sons: Balian, John, Baldwin, and Guy. Balian inherited Beirut. John inherited Arsuf. Baldwin married the sister of Amalric of Beisan and became Seneschal of the Kingdom. Guy married the daughter of Amalric Barlais (who'd been reconciled) and became Constable of the Kingdom.
There were other relatives beyond John's immediate descendants. The Count of Jaffa was his nephew and was the author of the Assizes of Jerusalem, a major legal work. Balian of Sidon was another nephew and was bailli in the Kingdom. Philip of Montfort, another nephew, was brother to that Simon of Montfort who led the Albigensian Crusade. He married Maria, a princess of Armenia who was also daughter of Raymond-Roupen and the heiress of Toron. Yet another nephew was John of Caesarea.
Despite all this, Filangieri held Tyre and Tripoli, and he was generally left alone.
The Crusade of Thibaut of Champagne
Another crusade arrived in 1239 when Thibaut of Champagne brought an army to Acre. He had great hopes, but managed to the wrong thing at just about every step. He had only good intentions, but was so ham-handed in his relations that most everyone was glad to see him leave again.
He marched on Ascalon 2 November. On 12 November one contingent of the army, acting rashly, got into a battle near Gaza and was routed. This forced the main army to break off its siege of Ascalon and return to Acre. On 7 December an-Nasir drove the Christian garrison out of Jerusalem in revenge for an earlier attack on a caravan. There followed a complex series of alliances and treacheries that managed to prevent anything meaningful from getting done.
Thibaut left Acre in September 1240. He'd managed to recover Beaufort and Safed, which were important castles, and Ascalon was ceded back to the Christians.
The Crusade of Richard of Cornwall
Less than a month after Thibaut's departure, another crusader army arrived, this one led by Richard of Cornwall. He was even better positioned to accomplish something than Thibaut had been. His sister was married to Emperor Frederick and his crusade had the Emperor's full support. Frederick even authorized Richard to conclude treaties on his behalf.
But his army was nowhere near large enough. He was a good negotiator and was well respected. He made a few desultory military demonstrations, but mainly his gains were through diplomacy. These included acquisition for the Christians of Mt Tabor, Tiberias, and the castle of Belvoir. Richard left in May 1241 with the Kingdom seeming to be in better shape than it had been in a long while.
But that was an illusion, for there was no central government to speak of. The Templars and Hospitallers acted like independent states, making and breaking treaties as they pleased. The Commune of Acre whent its own way, and Filangieri was still in Tyre, still making attacks when he could.