Must the suitor abandon his cousin after their marriage became impossible due to her uncle's refusal to let him reside in his home?

The wedding feast (walima) in a marriage is recommended, not obligatory. It is recommended that it be commensurate with the husband's financial situation, without extravagance or wastefulness, as Allah says: "Allah does not charge a soul except [with that within] its capacity," and "And do not be extravagant. Indeed, He does not like those who commit extravagance," and "Indeed, the squanderers are brothers of the Shayaṭīn (devils)."

The Prophet (peace be upon him) hosted a feast of ḥais when he married Safiyyah, and he said to Abd al-Rahman ibn Awf, "Give a wedding feast, even if it is with a single sheep."

Based on this, the wife's family does not have the right to delay the consummation of the marriage because you did not hold a feast beyond your means. You have the right to hold the feast in your own home. If they insist on their stance, and if you can meet their request without committing something unlawful, then do so to preserve the family. If you are unable to, then weigh the harms of divorce against the benefits of keeping the wife, consult with people of sound judgment and righteousness, seek guidance from Allah (istikharah), and do not rush into a divorce decision until you despair of finding another solution.