How to sort nodes per domain with the Views module?
You are right: Best ot achieve ordering in views-lists is indeed draggableviews. But beware that this doesn't work with all styles. I am not sure, since it is half a year ago I have needed it for a project, but I think draggableviews is made for tables in mind. But as far as I remember there was an additional module making it possible also for other listing styles. 

But the rather real problem is not how to order the views list items. The problem is that you need 2 almost same but a little bit different views (page-views? or block-views?), and how to let the 2 views show up on 2 different domains. I assume you would like to have the kind of same page on the same path but on two different domains in two different orders. The problem here is, if you try to achieve this with overriding paths by 2 different views and different domain conditions, the filtering or conditioning of the view depending the domain will make some trouble... It will always try to load both views and will always take the first arriving and if the condition doesn't fit, it will not change to the other. This is not a bug. It is because of how overriding paths works. 

Let me know if you have any idea how to achieve this last part. Maybe I can help then on some further steps on it. But in the moment I see the end of the road here.