When you have the camera in your hands, you are in control. You decide everything, and you can change anything in an instant. It is a fluid process.
When you are in front of the camera, you have given up control and the process has become rigid. Thankfully, the task is not impossible.
First, everything you know about photography still applies. Just because you are in front of the camera and not behind it, does not mean that you don't have to consider composition, lighting, depth of field, etc. You still need vision.
A tripod is a very useful tool. If you don't own one, you can use a flat and sturdy surface instead. You'll want to adjust the composition and all of the settings to how you want them prior to photographing your family. Take a few test shots to make sure everything is right.
You can use the camera's self-timer. The problem with this is option is that you are running back and forth, and by the time the timer finishes and the shutter opens someone is not cooperating (especially if you have young kids). Because you are quite aware of when the photograph will be taken, there is a tendency to look unnatural. Give yourself plenty of time if you use this method because you'll want to give yourself a lot of tries.
Another option that is better is to use a remote. You control when the shutter opens. You will have better luck capturing the "moments" and so the images will look more natural and less staged. The problem with this method is that you have an object in your hand and that may show up in your photographs.
One other option that I really like is to use interval shooting if your camera has this setting. I found that having the camera automatically capture one image every five seconds is ideal. Because you'll be capturing a lot of photos, it will take only a few minutes to get some good ones.
I used 11 point autofocus for these photographs, and the camera got the focus right on almost every image. Also, while I might normally use f5.6 (or larger) aperture for portraits, I used f8 for these just to make sure the depth of field wasn't too shallow (better to have too much depth of field than not enough).
Most of all have fun. Relax and laugh. Don't worry too much about everything being exactly right. Capture the joy and love that your family has. That is how to be successful.