Is it reprehensible for someone to prepare dinner for his relatives and send his brother to buy the supplies, then count the remaining money afterwards; and is it considered reprehensible to meticulously check the remaining money to verify the correctness of the account?

Counting something is not blameworthy; in fact, it can be praiseworthy. The Prophet, peace and blessings be upon him, estimated the fruit of a woman's garden. And Allah Almighty's saying, "أحصي" (Aḥṣī), means: "Memorize the number of its كيل (kayl - a measure of volume)." This has no relation to the hadith: "Do not count, lest Allah count against you." The meaning intended by this hadith is counting things for preservation and hoarding, and neglecting to spend in the way of Allah.