Looking up "Lover's" on the in game console actually shows 2 magic effects called Lover's Comfort: CDA1F and 10D96C. This implies that while they share the same name, those two effects are considered different, so yes, they should stack with each other with no problems.
Even though there are two versions of the effect that can be seen in the console, the version that is applied from the spouse and the stone are the same (could be a bug), so currently they do not stack.
This happened to my wife, Aela the Huntress, when I got married.
What I found out, is that she teleported outside Riften's walls, and then began a slow walk back towards Jorvaskyr. (I could track her location because "Ask the leaders of the Companions about Work" was in my questlog).
Perplexingly, when I fast-traveled back to whiterun, I saw Vilkas and Farkas (who were both at the wedding) but no Aela. For whatever reason, she was traveling more slowly than any of us.
What this boils down to is that your newly wed wife is going back to her default location - so you were right to check the pub where you originally hired her - but wives tend to go about this extremely slowly.
My suggestion? Wait a few in-game days and then check the pub again.
Best Answer
Yes you can: source from the Elder scrolls wikia
The above suggests you need to use some console commands too, but most people are reporting that you just need to put her down and remarry.
Update: I just found this on UESP
So it seems very hit and miss.