I just spent fifteen minutes doing nothing but repeating this phrase over and over! I must have said it over a hundred times! It would usually recognise « Demain dans » but not once did it recognise « l'après-midi »! I tried playing back her voice and using some recordings from Forvo.com but not even that worked!
« J'aime dormir l'après-midi » is a general statement: "I like to sleep in the afternoon(s)". Another translation that's not as good would be "I like to sleep afternoons".
« Demain dans l'après-midi » is a specific statement: "Tomorrow in the afternoon". I believe "Tomorrow afternoon" would just be « Demain après-midi », the same way that "Last night" is « Hier soir ».