"Happily" doesn't really fit here. "Luckily" - yes. "Happily" isn't used to express luck but more an emotional state. "Happily he returns tomorrow" can only mean that he is very happy that he returns tomorrow. This example's sentence means that it is a good thing he returns tomorrow. "Fortunately" means it's a lucky occurence, which may or may not imply happiness.
Very good response. I guess that native speakers often make so many grammatical mistakes that we're not even aware of making them until someone points it out. I have learned a lot about my own language here on Duolingo as well as other languages. I might say "happily" in this context because I hear it so much, but it's not correct.
Shouldn't thankfully work? In Spanish "Felizmente, el regresa mañana" would be something along those lines. Happily is one thing I honestly am not acquanted to have seen in either practice (I'm Mexican by the way) or literature. In that case it would be "alegremente" and that would sound odd (Yoda like, that would be :P)