Kelly- there is a lot of information on this site about the Jungfrau region:
A lot of the subheadings are informative.
You can drive to Lauterbrunnen and park. Large garage.
Cograil up from there to Jungfraujoch.
You can also drive as far as Grindelwald- not as much parking. Cograil up from there as well.
This guide helps a lot about the region.
If you have a few minutes space in your itinerary to spare, the area is a candidate. However, April is still ski season. Higher trails are not clear for hiking until about June 1. Would not be surprised to find some hotels closed for between season break.
Lauterbrunnen valley will be accessible, but should have snow on the ground.
As a rule, high alpine passes open in early to mid June. I have never tried to access the Gotthard tunnel in snow season, but it is surely possible. It is not my personal style to like the long tunnels. I'd rather ride a train, but the truck drivers do that tunnel all the time. You'll have company.
The train ride through the Gotthard Pass from Flüelen to Bellinzona and onward is really spectacular. I'd rather ride the train and not have to drive through a long stinky tunnel. All members of the party can move around, look out both sides, get a bite to eat, etc.
<<"We would like to drive through a tunnel called gotthard, unless there is a better tunnel to see?">>
What are your criteria for choosing a tunnel?. Switzerland has about 1 zillion of them, of varying lengths, altitudes, etc.
<<"we would like to see the mountains up close. Should we park the car somewhere and explore by train ?">>
There are a lot of spectacular ways to do that by train. Short trips, day trips, long rides. How much time have you allotted?