I was watching Alvin and the Chipmunks: The Road Chip in which there are a a lot of lame scenes (for example when they sing Conga as an answer to their owners words), and I felt really embarrassed. Or the same happened in Smurfs when the smurfs are standing up against Gargamel and sing their "war song". (Check it out on youtube.) I exampled children's movies, but I feel this in case of a lot of badly written movies/books. I wouldn't call it cringe or second hand embarrassement, because I don't feel embarrassement for anybody (being humiliated), I feel embarrassed because what I watch is very lame. Thank you for helping me! :)
Cringeworthy is the word you want.
If it has to be a single word, cringeworthy fits the bill: "something so embarrassing, it makes the viewer / listener / audience cringe…"
If a single word isn't really necessary, why not simply say "embarrassingly lame"?