I don't think the church sees sedevacantists as a problem in need of fixing, honestly. It's a small group of people. It comes down to that, all the while we are told by those loyal to their supreme pontiff, that the papacy isn't the totality of their church. What else do you have in common?
The Roman Church seems content to continue liberalizing (whatever that means), so I think it's content to leave Traditionalists behind. BUT, I think the Church does see itself as a "big tent" where traditionalists and charismatics can co-exist so long as each says they're loyal to the Pope. The communion, then, is based on fealty to the Pope and not shared liturgy or faith. I think that's the way it's heading but others will surely disagree with that assessment.
I don't even think that those on the far sides of the spectrum have in common the fealty to the Pope. But, remarkably, merely saying they do is enough.
On the whole, though, for the vast majority of Catholics, what they have in common is only submission to the Pope. Of course, they don't agree on what that submission entails.
In a perfect world, I guess, there would be an agreement on the faith, but the Eastern Catholics on this forum have demonstrated this isn't the case as far as I can tell... But that's another issue, I guess.
I describe this current idea of communion as a merely visible communion instead of a union of the faith. And even the visible communion isn't always expressed in a common way since, again, you can have a bishop say a Solemn High Mass one week and a clown Mass the next. I think these evidence a different theology, but Rome apparently doesn't see the conflict.