Malcolm is driven by morality when he tries to take back Scotland. As Duncan’s successor, he is basically responsible for the kingdom.
Now that his father is dead, Malcolm would be the king if Macbeth did not take the throne.
We will establish our estate upon
Our eldest, Malcolm, whom we name hereafter
The Prince of Cumberland (Act 1, Scene 4, p. 18)
Malcolm is genuinely distressed when he realizes that his father is dead. He decides to flee to England, and his brother to Ireland. Once in England, Malcolm bides his time until he can return to the throne. He gathers support, including Macduff.
When Malcolm is vetting Macduff, he wants to see if he is really loyal. He pretends he is too young and lusty to be king, and that he would be tyrannical and steal both money and daughters from his subjects.
Nay, had I power, I should
Pour the sweet milk of concord into hell,(110)
Uproar the universal peace, confound
All unity on earth. (Act 4, Scene 3, p. 69)
Malcolm is more concerned with making sure that his kingdom is returned to normal than getting power for himself. When Malcolm heads for Dunsinane, he has many supporters.
Most people do not like Macbeth’s rule. If Malcolm were ambitious, he might have tried sooner. He waited until he knew he had the support. He also does not kill Macbeth himself. He allows Macduff to do it. He isnot there to get revenge.