I currently have part of the book, but the first 30 pages are missing. Also the binding is worn away and the final pages are missing. The book is a collection of folk tales, fairy tales, nursery rhymes, etc. I always called it the Wolf Book, but I’m sure that is not the title. It was published around 1950 at the latest , but could have been considerably older.
Some of the stories in it are: The Three Little Pigs, Chicken Little, The Lion Hearted Kitten, The Hole in the Ground, The Gingerbread Boy, The Three Sillies, The Tortoise and the Hare, Little Red Riding Hood, The Cap that Mother Made, The Boasting Bamboo, The Musicians of Bremen, Silly Will, Hans in Luck, The Ugly Duckling, and many more.
Are you sure you aren’t confusing two anthologies? That is, plenty of those stories – especially The Lion-Hearted Kitten – are in The Illustrated Treasury of Children’s Literature (1955). See here – you have to scroll 1/4 down, and there are two entries, right next to each other. (However, I’m sure that five of the stories you listed are not in it.)
http://www.loganberrybooks.com/solved-ij.html
For some reason, that is not at the Anthology Finder. There may be more than one dust jacket.
But…the only time I saw The Cap That Mother Made was in a 1920 edition of My Bookhouse. But then, I’m only familiar with about ten of the MANY anthologies listed here:
http://w1.loganberrybooks.com/books/authors/anthologies.htm
To find My Bookhouse, scroll down about 2/3.
Possibly one of Watty Piper’s books. Folk Tales Children Love has The Cap that Mother Made.
There’s a possibility it might be Georgene Faulkner’s ‘Road to Enchantment: Fairy Tales from the World Over’, 1929.