So much of learning photography nowadays is spent on the technical aspects of the camera (shutter speed iso aperture), and also the “rules” so to speak, such as rule of thirds or filling the frame etc. I see very little on the basics of light. Most of the togs posting for critique to this site photograph people, and most of them all have the same fundamental problem – poor light, or their inability to recognize it. But hey, they put the person off to one side (rule of thirds), and shot wide open to blur the background(aperture).
Looking at the Lee family shots, the little girl holding the pink soccer ball is probably the best shot lighting wise because of a few reasons. The light appears soft, and by tilting her head up you opened up her face and eyes to it as well. There’s also a nice back light or “kicker” from the sun hitting the left side of her head which helps with separation from the background. Add a great smile and you have a very nice photograph.
Looking at the family photos, that’s were things fall apart. As Coastaltog said, some sort of fill flash or reflector is needed to even out the exposure when your background is much brighter than your subjects. My suggestion is to find an area where the background is the same or darker than your subjects, and that’s where understanding light will help. As far as shooting at F11, I’m going to guess your were shooting in program mode with the flash enabled. Unfortunately your camera (D5000) does not do High speed sync (HSS), so it has no choice but to choose a high aperture to keep the shutter speed down to it’s limit, as it pertains to flash. If you don’t know what that means then a primer on flash it needed. Check out this link http://neilvn.com/tangents/flash-photography-techniques/. One of the best resources on flash photography I have ever seen, including a section on how to properly utilize fill flash.
Any lighting course should be hugely beneficial, even a studio one, because(I hope) one of the main aspects they teach you is placement of lights and the different modifiers available to do great portraiture . You’ll learn lighting patterns, ratios, etc – all sorts of good things that can be applied to outdoor photography as well.