I’m sure you’re already getting this, but it’s going to be extremely difficult to satisfy everyone’s wants on a trip like this. I think you’ll be well served by scaling back your plans as much as possible. Six people, even setting aside the age gap, are likely to be on very different schedules. Getting folks to and fro, arranging meals (even deciding which ones you might have together versus not) is guaranteed to be herding cats. Your primary objective should be spending this time together with as little stress as possible. This goes double for you, because even with the most agreeable travel companions being the point person for them is naturally stressful.
With that in mind, I’d try to keep yourselves to two bases in Italy. Rome and Venice are the best candidates: beautiful places, plenty to do, plenty of tourist infrastructure, and neither really requires you setting foot in a museum to enjoy it. Both have a lot of day trip options around them as well. In short, they offer max flexibility. With five nights in each, you’ll have plenty of time to let people find their feet, plan activities together, and afford time apart. You can even establish a bit of a routine “meet for breakfast here at 9am everyday” and such so you’re not constantly in a state of figuring these things out. Another option is to start in Venice, you can spend a lot of time exploring the underrated towns of the Veneto region, then train to Milan for a couple days before further train to Switzerland. This is much more of a straight line and makes sense logistically. Switzerland is another bag I’ll get to in a moment.
Amalfi Coast should just be off the table completely. It’s the most complicated place to get around, and not easily accessible. You simply don’t have time. Since you’re not art/museum focused I would also just leave Florence off this itinerary. I’m kind of in the minority, but I don’t find the city of Florence particularly attractive. It’s quite tight, and landmarks aside the architecture can be bland. Basically, if you’re not negotiating the artistic treasures of Florence, then you can leave it out.
Now, Switzerland. I think there’s some sacrifices that need to be made. And Switzerland forum may have better thoughts on how manage this, but right now this is the toughest leg. Zermatt probably needs to go. Lucerne and Lauterbrunnen are close enough to Zurich (and Milan) that you could pull them off. But it’s still a jam, and is kind of assuming you’re flying out of Zurich. You may want to pull a day or two from Italy to give this some breathing room. I also can’t help thinking that May can be a little early for the Alps. It may be downright cold when you’re there. Is that what folks are envisioning? Do y’all want to pack jackets for that? I think there’s a great deal to consider here. While no one wants to let down your elders, if there’s one thing on the itinerary that should maybe get the axe this may be it. Either that or lean a little further into it.