I don't know that the bible should be your foremost source for deciding how to treat someone who has abandoned his family. Yes, include biblical teaching on charity and mercy as one of several important factors in your decision making in such a matter. However, IMHO, I think it would take God to show charity to such a person. Nevertheless, I will provide a context and intepretation for this verse, Matt 5:29
In the NT the word, righteousness, conveys recognition of individual righteousness. E.g., Jesus requires that our righteousness exceed that of the Pharisees or Scribes, or we shall not enter the kingdom of heaven, Matt 5:20. There is no thought here of entering heaven because we have obtained an "alien righteousness". The responsibility is on the individual to make sure his righteousness is true righteousness. Jesus explains how we can measure our righteousness, in the remaining context of Matt 5.
In verse 21, it is no longer sufficient to refrain only from killing someone; rather, Jesus says, that even being angry with another's brother puts one in danger of judgement; ie., judgment that results in not being able to "enter the kingdom of heaven" as he has just stated in Matt 5:20. Hence, the way our righteousness exceeds the righteousness of the Pharisees is by refraining from anger, whereas the Pharisees,tho they did not murder their brother, hated him and reviled him in their heart.
Again, interpreting the bibliical language for its face value, meaning within its own context rather than superimposing a theological system upon it, we learn that we do not exceed such Pharisaical righteousness by laying claim to someone else's righteousness [i.e., Christ's] but by exercising our righteousness by the power of God's grace unto the God who views us under His grace.
In the remaining context, Jesus tells us the many ways our righteousness can exceed that of the Pharisees, e.g., not looking with lust on a woman [verse 28], not divorcing illegitimately [verse 32], not swearing [v. 34], not seeking vengeance [v. 39], loving one's enemies [v. 44]. We must do these things, according to verse 45, "that you may be the children of your Father which is in heaven," not merely because we "are" his children.
Be with God.
Amen