Woah. That's a long wishlist. You cannot reasonably see all of those places in 12-1/2 days.
So let's prune the obvious: Murren. April is not a very good time of year for the Swiss Alps, it takes time (and $$$) to get there, and I think you'd want four nights on the ground in the area to have a reasonable hope of good weather for outdoor sightseeing. So no Switzerland on this trip.
Now we're down to two broad possibilities: Italy and not-Italy. Pick one.
The family reunion on April 15 complicates matters. I wouldn't want to range terribly far from the Madrid-San Sebastian axis for logistical reasons, so that looks like a good place to slide in Barcelona/Figueres. But what about Madrid? There are lots of great day-trip possibilities from Madrid even if you are not big fans of art museums (are you?). I think the top two side trips are Toledo (clearly #1) and Segovia. I also like Cuenca; others like El Escorial. So: what do you want to do about Madrid? What do you want to see there? It could fill all your time before you head to San Sebastian on April 14, unless you opt to do your Madrid sightseeing at the end of your trip instead (not a bad idea).
For me (who spent 10 nights there in 2016) Barcelona itself needs 4 nights (that means just 3 days of sightseeing), plus you need an extra day to get to Figueres. Girona would also be worth a day, as would Montserrat if you're lucky with the weather.
Then there's the possibility of seeing more of the Basque Country (Bilbao is very interesting), if you're up for what may be coolish/wettish/overcast weather.
As I write this out, I'm convincing myself that you should stick to Spain:
April 9: Arrive on transatlantic flight, sleep-deprived and jetlagged. Train to Barcelona (5 nights).
April 14: Travel to San Sebastian. Trains departing at about 7:30 and 10 AM take approx. 5-1/2 hours. At least two nights in San Sebastian, more if you want to see Bilbao, Vitoria-Gasteiz, Hondarribia, etc.
April 16 or later: Train to Madrid for the remainder of your time.
If you have no interest in Madrid's art museums or the Basque Country, I suppose you could skip Madrid and spend the rest of the trip in Seville/Cordoba.
