Felting is pretty easy once you get the feel for it. But it would probably have been easier if you tried for the first time with someone that knows what they're doing!
I've made lots of felt items, including lots of felt balls. I think the trick with the balls is to add only a small amount of felt on each layer. Start with a small handful, get it good and wet in soapy water as hot as you can stand it and really roll it hard until it is nice and firm. Then just keep rolling and adding thin layers. Keep the water hot and use lots of soap. It takes longer than you think. Some wool also felts more easily than other types. And I use laundry soap (not detergent). Some liquids might contain moisturizers or things that would interfere with the felting process. Sometimes you have to just press the wool on when you are adding layers, passing the ball back and forth from hand to hand, to prevent it from bunching up.
A great book to check out, actually two great books, are Felting by Hand, and The Art of Feltmaking, both by Anne Vickery (I think). Try to get them from the library.
Soon you'll be making felt slippers for your little one! It is a wonderful thing to work with wool. . . .
Good luck and let us know if you have more success!