You can pay for care outside the home for a child under 13. However, schooling is not allowed. I think, if audited, there could be an issue raised as to whether these programs were care so you could work, or were they part of an enrichment program for home schooled kids. (My daughter homeschools my grandkids, I have a pretty good idea of what you are talking about.)
Ultimately it is up to you if you think you fit the rules and could prove it. The rules are in the instructions for form 2441 and I copied some below.
https://www.irs.gov/instructions/i2441#en_US_2023_publink1000107923
Qualified Expenses
These include amounts paid for household services and care of the qualifying person while you worked or looked for work. Your work can be for others or in your own business and it can be either in or out of your home. Child support payments aren't qualified expenses. Also, expenses reimbursed by a state social service agency aren't qualified expenses.
Generally, if you worked or actively looked for work during only part of the period in which you incurred the expenses, you must figure your expenses for each day. However, there are special rules for temporary absences or part-time work. Also, if part of an expense is work related (for either household services or the care of a qualifying person) and part is for other purposes, you have to divide the expense. However, you don't have to divide the expense if only a small part is for other purposes. See Pub. 503 for more details.
Household services.
These are services needed to care for the qualifying person as well as to run the home while you worked or looked for work. They include, for example, the services of a cook, maid, babysitter, housekeeper, or cleaning person if the services were partly for the care of the qualifying person. However, they don't include the services of a chauffeur, bartender, or gardener.
You can also include your share of the employment taxes paid on wages for qualifying child and dependent care services.
Care of the qualifying person.
Expenses are for the care of a qualifying person while you worked or looked for work only if their main purpose is for the person's well-being and protection. It doesn't include the cost of food, lodging, education, clothing, or entertainment.
You can include the cost of care provided outside your home for your dependent under age 13, or any other qualifying person who regularly spends at least 8 hours a day in your home. If the care was provided by a dependent care center, the center must meet all applicable state and local regulations. A dependent care center is a place that provides care for more than six persons (other than persons who live there) and receives a fee, payment, or grant for providing services for any of those persons, even if the center isn't run for profit.
You can include amounts paid for items other than the care of your child (such as food and schooling) only if the items are incidental to the care of the child and can't be separated from the total cost. But don't include the cost of schooling for a child in kindergarten or above. You can include the cost of a day camp, even if it specializes in a particular activity, such as computers or soccer. But don't include any expenses for sending your child to an overnight camp, a summer school, or a tutoring program. See Pub. 503 for more details.
