@mike321321 OK, I finally figured it out. For anyone else who is having this problem.
Drill down in heart (bookmarks) to Bookmarks sidebar. Select Other Speed Dials Select the remote speed dial collection. Right click on an empty space in the speed dial collection, to get four item menu with 1. new folder 2. sort alphabetically 3. paste. 4 select all. Choose Select All. Now move your mouse/pointer over the selected site icons, and right click again. ONLY THEN will you see seven item drop down menu, with a "copy" option. Select it. Now go to your current speed dial, delete anything you don't want there, and paste the other machine's speed dial contents.You will still have to maintain the two collections separately, of course.
Now as a philosophical matter, this is crazy. While I imagine that a few people want to have separate link collections for different machines, most of us surely want to have access to a common set of links on any device we log into. Surely. Just because I'm at work, that doesn't mean I'm not interested in the things I'm interested in at home. Just because I'm at home, that doesn't mean there aren't some work links I need quickly. This is just a badly thought out way of managing links.
It's too bad because it's a pretty implementation and Opera is generally a pleasure to use.