Is it permissible to divorce an unjust wife without fulfilling her legitimate rights? Can the aggrieved party demand the dowry and the expenses he incurred? Is he obligated to provide for the wife and son in the event of their separation?

You should have sought a righteous wife. What you mentioned about your wife constitutes nushuz (recalcitrance), which necessitates following the Quranic steps for its treatment: admonition, abandonment in bed, and non-violent beating. If the wife's nushuz is established, her maintenance (nafaqa) is forfeited, unless she is pregnant or nursing, in which case she is entitled to maintenance for pregnancy and nursing, according to custom and means. However, the child's maintenance is not forfeited. If the wife insists on nushuz, the husband has the right to demand back what he gave her, in analogy to what happened with Thabit ibn Qays and his wife.