We are creating an iOS app (child/education) and would like to use a shopping cart concept for in-app purchases.
Users will select multiple in-app purchases simultaneously and have the total be added together in a shopping cart.
Will this be approved by Apple?
This is possible. But it is not practical. The user will still need to click on each individual item (even after being added to the cart) and be prompted to purchase it one by one. This is because you do not control the "checkout process" of an in-app purchase.
When you purchase an in-app item, a prompt will ALWAYS come up stating something like "Do you want to purchase one XXX for $0.99?" Basically it's sending a request to the server saying this user wants to purchase XXX item. So for every in-app purchase item you've registered on iTunes Connect, the user must purchase it one by one. This is an Apple mandated process, there's no way around it unfortunately.