Welcome to My Swiss Alps.
Luzern is a good base in general, excellent for the first time traveler. There are some things that Children might find interesting, too. In the following link, scroll down to see a listing for Lucerne ( which the locals spell as Luzern, since that is the German spelling and Kanton Luzern is in the German speaking region of Switzerland)
But not everything on your list is close by Luzern.
To help your planning, it is extremely important to know what time of year you will travel. During some months in Spring and Fall, the areas around the high alpine resorts tend to have few customers and visitors, so many (but not all) services and hotels can be closed for these "low seasons."
These links might be helpful, as you begin your planning:
and a map and a timetable can help you understand the distances, locations, and travel times:
By the way, the correct spelling is Jungfrau.
The Rhine is a long river, as you will be able to see on the map, and has many different aspects, not to mention smaller branches which feed into it, such as the Vorderrhein. It forms the northern border of Switzerland for quite a distance.
My Switzerland, the Federation's tourism site has a lot to say about the Rhine:
I note that you wish to "cover" the maximum possible. I'm not sure what "cover" means. Would it include riding through on a train, walking in a town, hiking through the countryside? Taking photographs? Do you have any specific interests or restrictions on your travel? How old are your children? Very young children might have health issues with the highest mountains....the air is very "thin" ...low oxygen concentration.