It depends. One of the requirements for claiming the child and dependent care expense credit is that the expenses have to be work related. To be work related, the expenses must be incurred so that you and your spouse are able to work or look for work. Additionally, the main purpose of the expense needs to be that it provides care that is for the well being and protection of the child.

For example, this after school program would be considered a work related expense if you and your spouse are at work during this time and there would be no one to care for your children if they were not participating in this program. However, sometimes after school programs include expenses such as food and entertainment and these expenses are generally NOT considered work related expenses for the purpose of calculating the credit. 

According to page 7 of pub 503, under the heading, "expenses not for care", "expenses for care dont include amounts you pay for food, lodging, clothing, education, and entertainment. However, you can include small amounts paid for these items if they are incidental to and cant be separated from the cost of caring for the qualifying person". 

Please refer to pages 6-7 of pub 503 under the headings, "are these work related expenses?", "care of a qualifying person", "expenses not for care", and "education" for additional information. https://www.irs.gov/pub/irs-pdf/p503.pdf

Please refer to the following FAQs to learn more about the requirements for this credit.