My daughter hates reading stories in which the mother or the father or both die -- which rules out most of the fairy tales. While we read a lot of modern children's literature, any suggestions for traditional tales?

Each ethnic community in Singapore will have their own traditional tales so perhaps you can find inspiration from the stories you grew up with? I grew up in a Malay household so I read and listened to stories of Sang Kancil, a clever mouse deer who used wit and tricks to escape his enemies, most notably, the Buaya (Crocodile). I can't find a published version of the English translation for Sang Kancil but this website has compiled and translated one of the stories, perhaps you can read to your child from here: https://duniyaku.wordpress.com/2014/01/08/sang-kancil-the-clever-mouse-deer/