Tragicomic is used often in Swedish (Tragikomiskt). There is a nuance difference between tragicomic and bittersweet. Bittersweet is when you daughter moves out to her own place,it's sad that your kid grew up but also great, it's bittersweet but not tragicomic. Tragicomic is when something is so screwed up that the only thing you can do is laugh at it.
Right. Bittersweet is about something that affects you personally, some experience that blends joy and sadness. Tragicomic is about some external going-on that you observe and react to like an audience member.
There's also the laugh-cry emoji, which can be used for both situations, I think.