Why can't you self host? I have a wordpress site, and everything is fine, I use noIP for a domain name and IP tracking. Everything is running on a raspberry pi 4, with 7TB of USB storage. Loading up the photos can be a little slow when we post a big adventure day out, but if you're patient, or have the means to put a more powerful machine on the job, it is the best way to share your lives with family. Wordpress has an option to ask the search engine crawler to not index the website, and it seems to work. When I post to the blog, I have an email subscription list for all my family, who want to be notified of a new post.

Xmpp server with account for family members? Personally, I host one, and keep favourites pics on a minigal nano, a php app to share pictures on my webserver

I mean, you can just use some simple hard drives if you just want something that works. You can get a terabyte for like 40 bucks nowadays.

Maybe don't share online?

We have a printing center in my area that prints high quality full color photos for 75 cents a page.

Google Photos works well except it is exactly what you don't want.

Have pictures printed and mail them. Use a family text thread.

If you aren’t gonna host your own digital files and you don’t want someone else to get their hands on em those are the options.