Embed galleries on other domains

Hello everybody

I am looking for a solution, so I can embed my galleries on other websites/domains, like you do this with a YouTube video or so.

But my developers keep saying, that this cannot be created in Wordress for my galleries.

Can this really be true?

Example.
You go to YouTube.
You find a video, that you want to embed on your website.
You find the Embed-code, copy it and insert it into your post.
An automatic videoplayer arrives in your post.

I want the same, in this way:
I create a post.
I create a gallery, and put it into the post.
I share an embed code with another website/domain.
The other website/domain paste this code into their post, and save.
The other website/domain show my gallery, on their website.

Is it really true, that this cant be done? I know it would cause a lot of server loading for our server if many external domains start to “feed/embed” our galleries. But for sertan reasons, I think it will be all worth it.

Thanks