Detailed Explanation

Visiting Day implicates the following eight laws.

1.Generally, the owner cannot despair from retrieving an article without discovering the loss.

2. As long as the owner has not despaired, one may not leave an identifiable object in an unprotected area.  

3. Identifying features include unique size, shape, weight, packaging, and quantity as well as other non-standard features [Choshen Mishpat 259:3, 262:3].
 
4. The finder should  publicize the find in a manner through which it is reasonably possible for the  loser to see  the posting. Examples are local public billboards, synagogues, local circulars and media venues [Choshen Mishpat 267: 3].

5. The mitzvah of Hashavat Aveidah requires the finder to care for the article and take measures that the article does not depreciate in the interim [Choshen Mishpat 267: 17]. Assuming the article has no sentimental value, if it will depreciate considerably before the finder is able to return it, the finder may convert the item into its present cash value and use it [Choshen Mishpat 267: 21]. 

If the finder has no use for the article, he or she must sell it and return the cash value to the rightful owner [Mishna Berura 443: 11].  Nevertheless, if the finder does not sell it, he or she is not liable to compensate the loser for the loss [ibid].

6. The finder must inconvenience him/herself and extend a reasonable effort to return the lost article [Choshen Mishpat

7. Nevertheless, the finder need not incur a financial loss in the effort to return the article. Losses are not limited to finances. For example, one need not compromise on other social responsibilities to perform Hashavat Aveidah. Nevertheless, one who is perpetually stingy about helping others will become cruel and eventually become needy whereby having to come on to others [Choshen Mishpat 267: 1].

Thus, as long as pursuing the owner remains a bother but does not yet cause the finder a "loss", the finder is required to do so. The Torah leaves the balance between the two extremes to the finder's responsible discretion.

8. The finder must keep unclaimed items under his or her guard until Elijah comes and identifies the owner [Choshen Mishpat 267: 15].  However, one need not keep a commonly accessible item ad infinitum. Instead, one may 'purchase it' from the claimant and put the purchase money aside until the coming of Elijah [Igros Moshe].

♦

Application:

The parcel Mrs. Miller found still belongs to Dani's parents. If Dani received the parcel, it is possible that he is too young to legally despair from retrieving it. If Dani never received the package, his parents do not know that it was lost and as such did not despair. Thus, Mrs. Miller cannot leave the item be nor may she keep it for herself.

Identifying features:
While most of the articles in the package are standard, the contents of the care-package as a unit were unique.
Thus, providing the content information is equivalent to providing unique identifying features worthy of retrieving the article.

Care for the article:
Included in Hashavat Aveidah is seeing that the article not become valueless. Thus, if Mrs. Miller reasonably assumes that the dairy cake will spoil before retrieved,  she should freeze it. Or else, she may buy it, enjoy it and leave its monetary equivalent.

Practically Publicizing Find:
Initially in the days of the Temple, we had a national central Hashavat Aveidah station. Once we dispersed throughout the Diaspora, publicizing in the locale of the find was the recommended and most practical manner of fulfilling one's duty. Thus, the local synagogue took on the compromised role of the national central meeting station.
 
Accordingly, leaving a note near the place of find and publicizing the find in one of the local camps could be sufficient. Thus, Mrs. Miller could give the parcel in to Benny's camp office and see to it that the office staff publicize the loss and return the package to the claimant who can define all the items in the package.
 
This is a simple approach which would not infringe on Mrs. Miller's social responsibilities back home in Scranton and would complying with the initial Diaspora protocol. (Arguably spending the night going through the hundreds of camps in the area would compromise on her duties back home.)
 
However, the great advances in transportation, a product of the industrial revolution, created challenges in locating losers by simply posting a note in the local area of find. Thus, while Mrs. Miller might not be required to do more, posting the loss in one camp will barely assist the loser if Dani is a camper in a different camp.
 
Nevertheless, the industrial revolution produced its own solutions. The legendary 19th century Halachic adjudicator, Rabbi Moshe Sofer a.k.a the Hatam Sofer ruled that the modern day equivalent to local synagogue posting is posting in a popular local newspaper [Choshen Mishpat responsa 122].
 
Arguably, today the use of the central HashavasAveidah.com site and providing Benny's camp information would afford the most effective way of publicizing the find.
Hopefully, Dani's parents would notice the posting sooner or later and pursue its retrieval.
 
As noted, Mrs. Miller should not leave the care package in the unprotected parking lot. Thus, if leaving it with the camp staff is not an option, she should take the package home with her, post the information on HashavasAveidah.com and safeguard the package until Dani's parents legally retrieve it.

Returning the Package
Mrs. Miller is not required to spend money to reunite the parcel with Dani's parents. Thus, Mrs. Miller is only required to send the parcel in the mail to Dani's parents, if they will pay for the incurred costs. If Mrs. Miller is unsure if they will do so, she is not required to send the package to them.