When I view your website on my own iPhone, the gallery's Splash Page is displayed as expected (please see the Screen Modes support section for more details on the Splash Page) but when I click the Splash Page to expand the gallery, I see the error 404 that you reported.
When a gallery is expanded on an iOS device, the gallery is expanded on a new page instead of on top of the embedding page (please see the Expand Gallery Behavior support section) and Juicebox uses the 'full.html' file inside the gallery's 'jbcore' folder to display the gallery.
It looks like the 'full.html' page is not present on your web server when viewed on an iOS device (but the 'full.html' page can be seen on a desktop browser so it is clearly there).
The problem appears to be with access to files inside the 'wp-juicebox' folder when viewed on an iOS device.
If I try to view the 'readme.txt' file directly inside the plugin folder ('wp-juicebox/readme.txt'), I can do so from a desktop browser but not from an iOS device (I have tried my own iPhone) where another error 404 page is displayed.
If there was a problem with the file's permissions (too restrictive), I would have expected to see an error 403 rather than an error 404 page (and this should be consistent across browsers).
Try asking your web host why it is not possible to view this text file on your server from an iOS device:
https://www.sunsoft.com.au/wp-content/p … readme.txt
If they can figure this out, then it should hopefully resolve your problem.
Things I would check and try myself:
(1) Check your web site's .htaccess files(s) for any device-specific rewrite rules.
(2) Check the permissions on the WP-Juicebox plugin's files and folders. (Default permissions of 644 for files and 755 for folders should be fine.)
(3) Make sure that everything (WordPress, WP-Juicebox and Juicebox-Pro itself) is up-to-date. I notice that you are using Juicebox-Pro v1.5.0. You might like to take this opportunity to upgrade to v1.5.1 as many bugs have been fixed since v1.5.0. Please see the Version History for details. Full instructions for downloading the latest version can be found on the Upgrading Juicebox support page and instructions for upgrading the WP-Juicebox plugin can be found on the plugin's own support page here. (I really do not think that upgrading Juicebox-Pro will resolve your problem but I reckon it is probably a worthwhile investment of 5 minutes of your time.)
I hope that my notes above help to point you in the right direction.
Please let me know how you get on. Thank you.