Is filing a lawsuit to claim payment for two years of work—including contracting, driving, and coordination—in return for unfulfilled promises of support and the purchase of a new bus, considered seeking one's rightful due?

If the intent behind the question is to file a false lawsuit in order to obtain a right, then this method is Islamically forbidden. Ibn Taymiyyah and Ibn al-Qayyim have explicitly stated this, mentioning that using an unlawful means to attain a right, such as presenting false witnesses, is considered forbidden even if the goal is to secure a right, because lying is forbidden. The proof for this is the Hadith: "Return the trust to the one who entrusted you, and do not betray the one who betrayed you."