First of all, don't blame others for this mistake! Why on earth did you enter their nick names when making the reservations? - you didn't know that your inlaws had different christian names?

It is true that names cannot be rectified now - this has nothing to do with codeshare flights or not.

Anyway, this is unlikely to cause any problems at check-in (unless you keep chasing this). Gianni instead of Giovanni is def. not going to cause any issues (only 1 letter is missing). Suzy instead of Susan will most likely pass as well (2 letters are wrong and 1 letter missing). My best advice is to leave it as it is - and hope for the best at check-in. Your in-laws are not to mention this at all at check-in and most likely the agent will never notice the mistakes.