3 days in switzerland

3 full days and 2 half days (thats the way i understand your itinerary), with 2 cities, and 3 mountains / mountain areas is too much in my opinion. i would leave out at least one place (probably zermatt, as its more "out of the way" than the other places).

also, even if you have a car, i would travel by public transport. you cant travel up pilatus and jungfraujoch by car obviously :-). also, it would be nice to take a boat trip on lake lucerne. of course you can travel by car to kriens for example and take the cable car from there, but for me it would me more relaxed to use "only" public transport.

you might also want to consider the weather. if the weather is good, pilatus is good and you can enjoy great views from the top of the mountain. if the weather is bad, you will not see more than a couple of meters away, and then there is no point really to go up the mountain.

I fully second Nathalie.
You have a car and want to go to places which are hard to reach by car or which cannot be reached by car at all.
Jungfrau:
You can go by car up to Grindelwald (2 hrs OW, fuel cost 26 CHF). From Grindelwald to Jungfraujoch and back you will have to take the train: standard fare 177 CHF/pax
If you do all by train, you can buy a Bernese Oberland Pass for 230 CHF plus a discounted Jungfrau ticket for 60 CHF.
The Bernese Oberland Pass grants you free rides from Lucerne to Berne - Brig (starting point of the Zermatt railway too
The car drive from Lucerne to Zermatt lasts 5 hrs OW (4 1/2 up to Taesch plus shuttle train); the fuel costs are around 100 CHF

Like the others, I think you are taking on too much, especially if somehow Zurich gets into this itinerary. Note, given the time of year, consider that you could still have snow issues if you are driving in the mountain areas. Also if budget is a concern, understanding that it is thought of as a tourist highlight, I don't think the Jungfraujoch is the best bang for the buck, not to mention that it eats up a fair amount of time and, as mentioned by others, you better be sure the weather is good up there before heading up. Consider as an alternative Maennlichen and Kleine Scheidigg where the views are fabulous as well even if you are not as high up in the mountains. Of course, the Jungfrau is a great adventure, just not sure it fits with your time restrictions.