Question

What is the correct procedure for handling church offerings? Is it proper for several family members alone to count the weekly offering, make the deposit, and report annually to the congregation? Should we express our concerns to the session?

Answer

This isn't a theological question directly and the Bible doesn't provide a direct answer. But it is a matter in which the Church needs to be above reproach, and her officers beyond being accused (even falsely). Here is a paragraph on handling offerings from Planting an Orthodox Presbyterian Church which may help.

Handling offerings

The handling of church offerings is one of the most obvious and public displays of the administrative organization of a mission work. Clearly identifiable offering plates, bags, or baskets should be obtained and used right from the start of public worship services. A consistent procedure needs to be followed in rented or borrowed facilities for handling the collection and temporary storage of offerings. A plan should be in place to ensure that offerings are never counted in an informal manner or in a public location, and that they are always counted and recorded by more than one person. It is also important to have a clear procedure in place for how offerings are deposited and how and where records of offerings and contributions are kept, including a schedule detailing specific persons responsible for those tasks.

This certainly is a matter that should be under the oversight of the Session so a letter to them would be appropriate; the matter then becomes their concern and their responsibility.