Is the wife obligated to tolerate the neighbors' intrusiveness and their frequent use of her home because of the Prophet's (PBUH) exhortation regarding neighbors, or does she have the right to be upset about this situation?

If the wife is the one who rented the house with her own money, then the decision regarding it is hers, and the husband is not permitted to give the key to anyone except with her permission. If the husband is the one who rented it, he is not permitted to give the key to anyone as long as the wife resides in it, because she has the right to an independent dwelling that no one from the husband's relatives or other non-mahrams shares with her. They must fear Allah concerning their wives and preserve their privacy, and they must take the key from anyone who is not a mahram. The wife must demand this from her husband and adhere to the lawful hijab in front of all those who are not her mahrams.