Portrait photography isn't easy - just pointing a camera at someone isn't generally going to get you an happy photo.  What can you do to increase the number of quality photos you like?

Take Lots of Photos! If you expect every photo to be perfect, you can pretty much guarantee every picture will be at best mediocre.

The longer the focal lengths the better chance you have for isolating your subjects.   And when using longer lenses, used at large apertures (like f2.8) as well.  This will give a pleasant out of focus background without being too heavy.  For larger shots, shorter lengths are helpful (70mm).

Focus is always a bit of a challenge.  With  children, they often get very close, and the closer they are, the harder it is to focus.  To make matters worse, you really need the eyes to be in focus - when doing close ups the nose and ears are often on the edge of focus.    

The better shots are more often made than captured - set your self up in the right place with the right gear and the correct setting and then take lots of photos.  An age appropriate playground is good because people tend to loosen up and forget you are there with a camera.