Short hops within and outside of Switzerland

You do not say if you want to travel by car or train, but, if you are staying in Basel city (which I recommend) you do not want a car. Basel is one of those cities where a car cannot be used and costs money to park. Basel has an excellent public transport system.

1) Zürich airport to Basel is only 1h30 by train. That trip is so short it is not worth stopping anywhere in between, especially as you will be encumbered by luggage. Places to stay for one night are Luzern, somewhere in the Berner Oberland (Mürren, Lauterbrunnen, Wengen, Grindelwald). But all those are further from Zürich or Basel, not in between.
Luzern is ~1 hour from Basel and can be done as a day trip. Berner Oberland is further and too far for a day trip.
Glacier Express is not practical because it is not going your way.
For 74-year-old-Mum, perhaps Luzern is the easiest option.

2) Do not get a pass. Just buy normal tickets. While you are staying in a hotel in Basel you get a pass for free transport within Basel and suburbs. There is lots to see in Basel.
Day trips: Colmar, Freiburg im Breisgau, Strasbourg. All easy by train from Basel.
Plus a few smaller local "cute" destinations.
Yes, Paris is possible. 3h30 by train from Basel.

The Swiss pass is only valid on Swiss Railways, not valid in France or Germany. But, that is not what you want. You already have free transport in Basel. For trips outside Basel just buy normal tickets.

3) Luge, there is one in the Black Forest, but I have no idea if it will be open.

I have typed enough - Don't hesitate to ask (or send me a message) for more details.

If you visit Luzern, your kids might enjoy this http://www.rodelbahn.ch/?lang=en - the longest "summer luge" in Switzerland, right at Mount Pilatus. I believe it opens in mid-April so should be possible to visit. Of course it depends on the weather, as they will not open in bad conditions. You can also picnic there.

The Swiss Transport Museum in Lucerne is very popular. It's not my sort of thing, so I haven't visited it myself.

Sorry I forgot to mention we will have no car. So travel by public transportation only.
I should correct myself and say that I mean a detour between Zurich and Basel, not necessarily in between for a night just to maximize what we can see in Switzerland since I think some scenic sites are going to be farther away from each city anyway.
Thank you for the recommendations.

Chris, where are some "cute" local destinations near Basel you recommend since we are staying mostly in Basel?
One more question, any recommendation for scenic trains with the big windows? Would love to see the Alps via train.

Local destinations:

• Upstream of Basel (east), the next towns on the Rhine: Rheinfelden, Bad Säckingen, Laufenburg, Waldshut. There are parallel rail lines on both sides of the Rhine and these towns can all be reached by local trains from Basel. The first 3 are on the river and have bridges you can walk across. Start with Bad Säckingen. It has a wooden bridge which I think beats the more famous one in Luzern. Photo: https://upload.wikimedia.org/wikipedia/commons/d/da/Holzbruecke_Bad_Saeckingen_01_09.jpg
• For travel in Germany, buy a "Baden-Württemberg-Ticket", this gives unlimited local train and bus travel for a family in the state of Baden-Württemberg for one day. Price: €23 plus €5 per extra passenger (max. 4). This is valid from Basel "Badischer Bahnhof" (German Railway station). Details: https://www.bahn.de/p/view/angebot/regio/regionale-tickets/bawue/bawue_ticket.shtml?dbkanal_007=L01_S01_D001_KIN0014_lt-bawue_LZ01
• Into the Black Forest. Many good places to visit with a car, but without I suggest the following loop. Local train to Freiburg, another local train to Titisee (nice ride up a gorge). Spend time in Titisee (town+lake), then get a bus back to Zell (goes over Feldberg pass), from which you can catch a different local train back to Basel.
• Basel Zoo, for the kids.
• One or two days get a car, and investigate the Route de vin d'Alsace. Website: http://www.alsace-wine-route.com/
• Écomusée d'Alsace: http://www.ecomusee.alsace/en/ Outdoor museum of rural life with lots of hands on demos. Needs a car
• Haut Koenigsbourg (castle): http://www.haut-koenigsbourg.fr/en/ Possible with train+bus, easier with car and you can combine with Route de vin d'Alsace.

Thank you everyone! This has been very helpful! Any good tips on "reasonably priced" local foods in Basel or any ? We will have a kitchen at our apartment but will probably try some authentic foods by eating out. Should I prepare some cash for small shops or every places accepts credit cards?

Actually I have another question...given that we are going end of April, early May, are there moutain regions that are not worth visiting given our short time? I read on this forum that during this time Murren is not recommended because it is pretty dead at that time. I really was thinking of staying there so we can take the cable car to Gimmewald. Do you think it is worth it to say in the valley floor at Lauterbrunnen and go up the mountain for a day visit? I am also thinking of staying Interlaken, is that a better place to stay with shops to visit if the weather is not good? I guess my real question is, which is better for two day one night stay, murren, Lauterbrunnen, or Interlaken that has interesting things to see in town and not too far from the moutain if we want to go?

Susan