I'm really sorry to hear you had such an experience: Cinque Terre is one of my favorite places on Earth (especially Corniglia) and it's a shame if it gets ruined by things people could really make a small effort for. On the other hand, please consider that peak visiting times (like around Christmas) could actually bring out the worst of people, so be warned!
However: learning a sufficient amount of Italian to get around, not risk sounding impolite or, contrarily, swear like a sailor is definitely achievable in 10 weeks. Particularly so if you do speak French (especially in the Cinque Terre area, due to vicinity, French influences on the dialects are pretty strong), but it really depends on how deep you want to go.
In any case, even though I'm absolutely no teacher (just a native

) I'd be happy to help.