Hello Jo
which [public transport] pass should we buy?
First note that NONE of the Swiss Public Transport Passes are valid on the car trains through the Alpine Tunnels
Given that your stay in Switzerland is brief, and that you will have a car, investing in the all-Switzerland Swiss Travel Pass is clearly out of the question.
Lucerne
The minimum duration of a Lucerne Travel Pass (https://www.myswissalps.com/travel-ticket/lucerne-travel-pass/) is three days and currently costs 240 CHF per person. Clearly not worth it for your very short stay in Lucerne
Interestingly it might well be worth your getting a Saver Day Pass (https://www.myswissalps.com/travel-ticket/saver-day-pass/) for April 9th. The SDP will take you all over Switzerland, but USUALLY does not include lines which simply go up mountains. HOWEVER, the SDP is valid on the lines up Mount Rigi, (and on the Lake Lucerne Boats).
Now SDPs must be bought in advance. They can be bought up to six months in advance. So an SDP for 9th April can be bought in three days time….! I have just looked at the current price for an SDP travelling on the 6th April . It is just 52 CHF per person. That MIGHT be the price for Friday 9th.
Interlaken
The minimum duration of a Jungfrau Travel Pass (https://www.myswissalps.com/travel-ticket/jungfrau-travel-pass/) is three days and currently costs 210 CHF per person. Probably not worth it for your very short stay in Interlaken
The minimum duration of a Berner Oberland Pass (https://www.myswissalps.com/travel-ticket/berner-oberland-pass/) is three days and currently costs 240 CHF per person. Certainly not worth it for your very short stay in Interlaken.
On 10th April, I tend to support Anna’s second suggestion of driving to Grindelwald and going up to FIRST (https://www.myswissalps.com/activity/grindelwald-first/). If the weather is OK, you can easily spend all day at First.
If you are wanting more than one mountain top and your budget will stand it, come down from First after lunch, and then drive to Stechelberg via Zweilutschinen and Laterbrunnen. Park at bottom station of the cable car, and go up the Schilthorn (https://www.myswissalps.com/activity/schilthorn/) via Mürren. (Or just go up as far as Mürren.)
Best wishes
Roger