What? Gladness is a perfectly natural word in English — slightly more literary and less common in colloquial use than joy or happiness, but not rare or archaic by any means. As the Hollies sang:
I would, but it's actually really hard since lycka is usually used in its other sense, where it means "luck". You could easily make sentences like Han kände lycka hela eftermiddagen, but you could just as well use glädje there as well - not as a synonym, mind you, but they typically work in the same contexts.