Yes, there should be two accents.
Please, take a look at my comment about this issue here https://forum.duolingo.com/comment/17640617$from_email%3Dcomment&comment_id%3D31311947
I've noticed that some language have different terms for family as in immediate family (parents and children) vs family (in its entirety) In my native Dutch for example, we have 'gezin' for immediate family and 'familie' for family.
does this distinction exist in Greek vocabulary and if so, which one is οικογένεια?
No, Greek does not distinguish between the two with different terms. Hmm... actually, when you say οικογένεια you refer to people close to you but when you say συγγενείς (relatives) it's more general and could be distant relations. Σόι is kin, clan; it's a pretty common word in Greek. Οικογένεια may refer to people living in the same household or not - maybe people who at some point were part of the same household or extending to other generations (e.g. grandparents and siblings of parents). There's no clear limit though as to who can be included. How clear cut are the Dutch terms?
These observations about Dutch and modern Gk kinship terms are very interesting. Ancient Gk had a lot of kinship terms and for instance could refer to the family with οἶκος (the household, could include slaves) while συγγένεια was extended family, relatives, kin, somewhat similar to Spanish familia and familiares.
Family is considered to be a collective noun, so it's mostly (if not exclusively) used in singular. While in British English it's sometimes used in plural depending on context (depending on if the speaker refers to family as a whole or not), the course is for American English, and to avoid such ambiguities, we haven't included it in the translations.
(Edit: After further discussion with some native speakers, it was decided that it should be included in the alternatives.)
Keep in mind that this happens with many BE alternatives. Some of them even have different equivalents in Greek, so it's possible that their addition would cause confusion to natives and non-natives.