I'm still experimenting to find the right mix. I've tried Dropbox, Google Photos, Amazon Photos, a private site built from scratch, and a handful of paid private photo sharing sites. Haven't quite found one that I love yet, but I'm still experimenting and searching. Building a custom solution offers the most privacy, but it's hard to find the time to do it.
iMessage is my goto method for sharing kids pics these days. It’s on purpose to the people I know care and who I trust. Also private so no endless public record. And there are archived backups in the cloud. Perhaps some of my extended circle misses out this way? But it mostly seems to work.