In the sentence: Her head was in his lap, and he was playing with her hair.
Given that what the verb really defines is him brushing her hair with his hand or stroking it gently, is there a better way to express that ?
I don't think you can use one word to say "play with someone's hair", but I think the verb "to caress" does a better job of expressing the idea of him lovingly stroking her hair:
Her head was in his lap, and he was caressing her hair.
caress: to touch someone gently in a way that shows you love them
: to handle, stroke or touch lovingly AHD
The word cafuné in Brazilian Portuguese is literally "the act of fondling someone's hair". It's considered untranslatable to English, thus could be a loanword or borrowed word.
To "tousle someone's hair" is to play with someone's hair...