Discuss the quarrel between Cassuis and Brutus. How is their conflict resolved? What are the deeper issues and the misunderstandings between them?

In Act IV of Julius Caesar, Brutus and Cassius are engaged in a civil war against Octavius, Antony, and Lepidus. Brutus and Cassius meet to discuss problems in their ranks. Cassius is upset with Brutus because Brutus condemns a man that Cassius defends. Brutus is upset with Cassius because when Brutus requests money from Cassius, he does not send it. 

This is the superficial argument between them. The root of the argument is based in their roles in the conspiracy and assassination as well as their relationships with Julius Caesar.

Throughout the course of the play, it is evident that Cassius is jealous of Caesar. In Act I, Cassius describes Caesar as a "colossus" that "bestrides the narrow world." When he recounts a day that he and Caesar both attempted to swim across the Tiber River, he portrays Caesar as weak and crying " 'Help me, Cassius, or I sink!'"(I,i, 201). When Cassius is trying to persuade Brutus to join the conspiracy, he states that Caesar's name is not more respected than Brutus' (or Cassius' for that matter). It is this jealousy that motivates Cassius to plot against Caesar and turn Brutus against him as well. 

While arguing with Brutus in his tent, Brutus questions Cassius' motives (for the first time). He says, 

Remember March, the Ides of March remember:
Did not great Julius bleed for justice’ sake?
What villain touch’d his body, that did stab,
And not for justice?

These doubts resonate with Cassius, who once again feels as if he competing with a dead man. Brutus then explains that he is not afraid of Cassius' temper and he is annoyed that when he requested money from Cassius, he was denied. Cassius is visibly upset, and responds 

I did not. He was but a fool
That brought my answer back. Brutus hath rived my heart:
A friend should bear his friend’s infirmities,
But Brutus makes mine greater than they are (IV, iii)

Cassius becomes incensed by the accusation that his motives and actions are not noble, and bears his chest to Brutus while offering his dagger. Cassius then declares 

I, that denied thee gold, will give my heart:
Strike as thou didst at Caesar; for I know,
When thou didst hate him worst, thou lovedst him better
Than ever thou lovedst Cassius (IV, iii).

Once again, it is evident that the root of the conflict between Cassius and Brutus does not have to do with money or gold. It is about the dynamic between Brutus, Caesar, and Cassius.