Choose one naming pattern
You could use a simple folder name beginning with the year and month. Compare files before moving copies from different devices: similar-looking photographs are not always identical files. Avoid reorganising the entire archive in one sitting. Start with the most recent month and work backwards only if the method helps you find things without creating more work than it removes.
Separate sharing from backup
An album shared with relatives should not be treated as your only backup. Review backup and sharing settings separately in the service you use. Closing a link does not necessarily remove copies somebody already downloaded. Consider who should receive images of your child and what identifying details accompany them. Keep location information and personal documents out of public album descriptions.
Your next little step
Choose one idea that suits your family and try it at your own pace. Every family has different needs.
An example in practice
Create a trial folder labelled with the year, month and a short event name. Add a small selection of images. Ask another family member to find one photograph, and simplify any part of the system that needs a lengthy explanation.