1) Get into practice mode. In order for practice to "stick" the brain must be focused on the task at hand. Practicing with an unfocused and tired mind is actually worse than not practicing at all. Bad habits are reinforced, and skills are performed sloppily and are easily forgotten. Take a moment with your child at the beginning of the practice session to find out what particular goal they are working toward on each piece. This will both remind the student of what they need to be thinking about as they practice and allow you to monitor the practice session effectively.
2) Do one thing well. If time is very short, encourage a student to work on only one specific homework item. The catch is that they must do this one thing very well. A specific skill can be reinforced in as little as five minutes if done in a focused, deliberate way. I always prefer a student that practices intensively on one area and comes to their lesson with improvement in that area over one who was short on time and practiced non-specifically.
3) Practice when alert and rested. Practicing after rushing home at 7 p.m. from a baseball game and bolting down some dinner might not be the way to go. Choose a time when you or your student is most likely to be able to focus mentally. Practicing the piano correctly ought to be mentally tiring!
4) Use your assignment notebook. It's amazing how often I hear students tell me they've practiced a whole week without looking at their assignment notebook! Teachers typically understand the process they're trying to impart quite well, and using the specific goals I give you will allow you to progress faster and practice more mindfully. When I write "practice right hand alone - focus on slurs and staccatos" in a notebook, that is the essential practice goal for the week on that particular piece, not just a nice suggestion.
5) Consider your priorities. It is unlikely that a student who consistently lacks mindful practice time will succeed at the piano or any other instrument. Consider how important making music is to you and your child and what level of mastery they would like to attain. I certainly don't demand that every student become competition material, but I find that I don't enjoy or feel good about teaching students who coast along at lessons due to lack of time. (I usually find that the students don't enjoy it either.) Making music can be enriching, mind-sharpening, and a lifelong source of enjoyment, but baseball can be too. (I suppose.)
I hope you find a few of these tips helpful, and please know that I appreciate and recognize all the time and effort parents and students devote to successful piano study. You amaze me!
P.S. Here's one way to get into the "mind space" to practice. Lang Lang clearly knows what he's trying to accomplish with imagery in this practice session!