Patience is a must when creating the perfect image. Often it requires waiting just for the right moment. And patience is an absolute must when working with children and pets. Think through the photo before you shoot it. What do you want to capture? Once you have an idea and a location to photograph, then bring your children and pets out. Be spontaneous as you follow the action and don't worry if your idea needs to change a bit. You may need to change your own position in order to keep a desired background in view. Make the experience fun for you and your subjects. Continue to talk to your subjects to keep them connected to you and the camera. Be ready for the unexpected moments. Poses are nice, but capturing a natural expression or action is far better.
So it may seem easier for you to just hold the shutter button down on your camera and cross your fingers, and that is okay. If this is the approach you prefer, be sure to edit out all the images that are out of focus or look bad. It will be far more impressive to your family and friends if you only show the photos that turn out well. Posting the best images of the bunch will have a much greater impact. If you have editing software, take the time to crop out unwanted objects and crop in to the subjects. Lighten or darken the images. Many applications have fun borders and effects that may improve your image. Less is more when it comes to showing off your pictures. The important thing is to just have fun with it.