Choosing Multi-Country Rail Transportation in Europe

start by looking up the man in seat 61, he is your go to guide for anything about rail travel:
https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm

You have comparatively little mileage in Germany, and that country has day-tickets that sometimes are incredible bargains for groups traveling together, so I suspect that you wouldn't save much on the German part of your trip with a pass. Others here can provide more specifics since you've laid out the specific trips you plan to take. If you con't get input in this thread, you might ask about the German section of you itinerary on the Germany forum.

For your trip from Paris to Geneva, you'll want to take a fast train, which means you'll have to pay for reserved seats on top of the rail passes. France has seat-reservation quotas for pass holders, so there's a possibility you'll find tickets available but no seat reservations if you don't make the reservation very early. If you're willing to pin down the date and time of that leg well ahead of time, you may be able to pick up bargain-priced promotional tickets.

Swiss trains are expensive, but you may find that a Swiss half-price pass in conjunction with individual tickets elsewhere makes more sense than a multi-country rail pass.

It's also conceivable that the youth rail pass is your best option but individual tickets will be best for the rest of your family.

Eurail multi country pass "sounds" like a good thing until you put in the effort to research how cheaply you can actually travel WITHOUT it.

There's no need for the others to have a continuous pass, even if you do, nor for the same countries. What matters is that you each have a pass (or ticket) that's valid for the day and country you're in, and the class of car you're in (1st or 2nd). But I would not recommend a continuous pass if you'll be studying 3 or 4 days per week. The Global youth pass for 15 days in two months is cheaper than the consecutive options (currently $769 in 2nd class) and would cover a few weekend roundtrips (from Amsterdam or where?) before you meet your family.

As already suggested, your short, regional train rides within Germany could be covered by group day passes for the area. For your family, you could consider a 3-country Select pass for 5 or 6 days of travel in France, Switzerland, and Austria, $430 or $474 per person for adults traveling together (1st class). On passes for 3 countries or more, parents have to pay for first class, even if they sit in 2nd class.

[edited] Passes for 1 or 2 countries offer 2nd class rates for everyone. For instance, 5 travel days in just Switzerland and Austria would cost parents $317 per person (2nd class). If they buy a reserved, advance-discount TGV ticket from Paris to Basel, Geneva, or Lausanne (connection stations), then the 2-country pass would kick in from there (if starting use of a rail pass travel day).

Paris-Switzerland TGV seat reservations for pass holders are on the expensive side, but cheaper in 2nd class, or it's cheaper to reserve a domestic TGV to Strasbourg and make an additional train connection. You'll also need a Thalys reservation when you head toward Paris.

Eurail passes give you 25% discounts up the valley and mountains from Interlaken and 50% discounts on the higher points of Mt.s Rigi and Pilatus near Luzern (but covered partway if using a counted travel day). See What do Rail Passes Cover in Switzerland?.

The pages I've linked have more info for comparing both ticket and reservation costs in those countries. Faster trains like Brussels-Paris and Paris-Basel can be discounted with advance purchase. If you plan to do so about 3 months in advance of travel, then you could cut roughly 50% off the full fares shown on our maps.

I just popped over to the Eurail website to look at the various discounts in Switzerland. Don't think I've ever seen a website that gives you so much info and so few details. No wonder people come here and ask about what kind of discount can they get on various train journeys - Eurail doesn't really tell them anything concrete. The lack of any details of benefits is enough of a red flag to be warned away from this dubious "pass". As far as Interlaken is concerned, this sign posted clearly on the platform says it all:

http://4.bp.blogspot.com/-8Dn2IwhigM0/Vp0j6VYiXEI/AAAAAAAAPXg/Eif41KVqTFg/s1600/DSC_4938.JPG

Thank you to all of you for taking the time to reply and provide such useful links and ideas - I may look more into a 15 day global pass for myself, but it definitely sounds like it may be in our best interest to look at mix-and-matching something like a Swiss pass (or two country pass) with day tickets in Germany for the rest of the family.

Thank you all again for helping to point me in the right direction on this!