You can not show Google one thing and users to another. That is called covering up that is against Google's webmaster guidelines. Your could not:
- Redirect users to
- Redirect Googlebot to
In addition to having all your content in a domain for SEO, you want to have all your content in a domain for the brand. You want your users to remember more than the name of the course. You want them to remember that it was a course of your brand. This is particularly important because you have items for sale and you want users to remember where to buy them. If you ever create another course, you want users to take the opportunity to take it because they remember the high quality of the previous course they took from your brand.
Instead of a separate domain for the course, I would recommend putting it in a subdomain:
https://course.example.com/ That will associate it with the brand in the URL and allow you to adjust the hosting platform as necessary. I would still need to mark the course with the same logo and color combination and keep the store and course interconnected. Subdomains are not always good for SEO, but they are much better than separate domains, especially in terms of brand. See Do subdomains help / hurt SEO?
If you really want the content in a separate domain, you should accept SEO a little worse and a worse brand. The aspects of SEO are not going to be much worse. The brand problems are worse, in my opinion.
There are a couple of technical tricks that could work. Google allows:
- The same content available in both URLs.
- Canonical labels to tell Google what URL to index
- Redirect to non-canonical version for non-Google search users
Therefore, you could try placing the content in both places and placing canonical tags on it so that Google indexes it in the subdirectory. It would have to have all the links from the storage point to the canonical version (the subdirectory). The subdirectory would have to link itself.
However, the separate site could also link itself, so that if a user were there, it would stay there. Canonical tags in the separate domain would point to Googlebot to the subdirectory version.
The trick would be to take the users to the separate domain. Any user who finds their Google subdirectory would have to see the content there to avoid the cover-up. However, you could tell schools to use the URL of the course separately, and that may be good enough for your purposes. You can also redirect users (but not bots) that were not referred from a search engine. It could redirect according to the reference header or redirect registered users.