can't get it work, even though there are no external widgets in the site, only widgets from muse themes and content of our own, no mixed content.
What's wrong with the site though:
but it works on:
This is not a Muse issue. What you need is a server-side certificate and the respective redirect in your .htacces file. This ha to be dine manually, because Muse doesn‘t write a .htaccess file at all.
The 2nd URL is on Business Catalyst servers which has an SSL certificate. Your hosting server does not have an SSL certificate. Or if it does, it's not properly configured. Where did you obtain your SSL certificates?