Does it describe that reserved sort of smile, when you slightly raise just one corner of your mouth?
Or a smirk?
Or is it an idiom that shouldn't be taken literally?
片頬 means "one cheek" (one of a pair (片) + cheek (頬) = one cheek (片頬)). So, 片頬で笑う would mean to smile with only one side of your face (which I assume is what you meant in the first sentence of your question).
I don't think this on its own is an idiom, but after research I did find one idiom that contains the phrase: 男は三年に片頬笑う. It describes a man who only smiles like this very rarely (i.e. "once every three years") because smiling too much will damage his dignity.