Gee, Suzanne, you leave out all the good ones. Your nieces and nephews will love all those songs about death, adultery, illegitimacy, desertion, and the like. Well, you left out drinking - they'll like drinking songs. They probably won't show much interest in love songs. All those bad things you listed are a normal part of life, and kids tend to accept songs that speak of those things with a healthy attitude. You may want to try a Keyword (click me) search of our database. You'll find various ways to browse the database in the blue box in the upper-left corner of this page.
Animal songs might fit your criteria. One song that came to mind was MISTER FROG WENT A-COURTING (click). We have five versions of the song in the database, so Dick and Susan (the editors) have given it a Digital Tradition designation number to make it easy to search for. You can find all five versions if you put #306 in the blue Digital Tradition search box.
I haven't performed it for anybody yet, but I'm working up The HOUND DOG SONG. I suppose you could argue that there's violence in the song, but it's pretty tame. I think kids will love it.
Hope that helps.
-Joe Offer-