Howdy Beni,
I would love to help you with this.
It sounds like you nailed the problem with isolating it down to HTTPs. I just tried an oembed from your site with the HTTPS URL and it is working great for me. However, my server is configured to be able to fetch HTTPS URLs. A lot of web servers out there are not, and for them trying to fetch and HTTPS URL just won’t work.
Your available options here are either to use the HTTP URL, or contact your website host and ask them to setup the server so that WordPress can fetch HTTPS content. Many website servers have purposefully disabled HTTPS in their configs though. I can only guess at their reason, it would save some money in setup and CPU time. So you might not have a lot of luck getting your host to configure the server properly for WordPress. Your best option is probably to use the HTTP url.
Does that all make sense? Will that work for you? Please let me know.
Cheers!
– Brook