So my sylveon adopted a shiny shinx that had been rejected by its parents and is raising it along side her two eevee babies. The shinx is around the size of the eevees right now but when shinx evolves into a Luxio and luxray do you think there could be problems with the currently happy family?

Not at all! Pokémon are highly adaptable creatures. Think about how many of them form families within their own teams. A trainer can catch a wide variety of different pokémon—even pokémon whose elements are by no means compatible with one another—and those pokémon will still be able to bond with one another and see each other as great friends, if not practically family. Moreover, pokémon from the same egg group (as the eevee and shinx families are) often take care of other members of that same group, regardless of actual species. In other words, sometimes, an eevee and a shinx can actually be blood relatives, and the two pokémon would still get along quite well.

In short, barring conflicts that would have nothing to do with your shinx’s species or physical attributes (because no family is without its differences, believe me), your shinx should do just fine. If anything, you should likely be wary about the fact that it’s shiny, but given the other fact that your sylveon and eevee are all tame, it’s likely that even that won’t be an issue.

Best of luck and congratulations, anonymous!