Have now seen your additional comments. I would say that an online service would be worth using, especially one which is free, but as a backup to other storage methods.
As you have long term storage requirements, and data protection issues, I will make some suggestions via private message, rather than publicise how I'd recommend you store the data securely.
Almost immediately, however, I would be suggesting you keep the 'personal' details separate, so no names would be linked directly to the photos, ie keep a file with 'reference numbers' so for each child it might be the initial of their surname and a number. Then the photos would have names tied to the reference number, plus date, and so on. Then ensure photos stored using one method, the 'reference numbers' and name/ age etc, stored elsewhere.
Rather than reinvent the wheel, there may be another section on MN which would find other people caring for children in a similar, professional capacity, who can explain their methods, so you can see the pros and cons.