Hi Leonie,
It is the same library. The library is stored on an external drive, "my passport pro" of WD which I bought a week ago. I transfered the library from the computer to the drive. I made it my system library and the pictures and videos were sent to icloud. I can get them without problem from my ipad. And I could get them also from the computer. But then something happened. I found myself with one photo in the library instead of 35.000. So, before the weekend I reactivated icloud with one change: I clicked "Download the originals on this mac" instead of "optimize the storage of the mac". When I came back from the weekend my library had ONE photo more coming from the cloud or maybe from the computer, which make a total of two photos, plus one video which I had shot during the weekend, and was still showing 180 GB in the finder!!!! In the "About my mac" under the apple it showed on the drive 198 GO of photos without entering into the detail of what belonged to the system library and what belonged to other libraries. Figures are coherent.
Re the Time machine issue, "my passport pro" drive is selected as the time machine recipient, along with another drive. But I had it switched off during the weekend.
To sum up, 1/ I have no access to the 180 GO of photos stored in my mac, and the fact that one new photo appeared in the library in a span of 48 hours, not knowing if it comes from the cloud or from the computer, doesn't change the problem 2/ my system lib is recognized by icloud at least for new pictures . This being said, I am totally stuck....