If you click on the 'further information' link it shows where the train stops. I suggest you google some of these places and see what appeals (everyone has different interests). I visited Lugano in 2018 for a short time and enjoyed it - there are several other places enroute which may appeal, for example, Como, Bellinzona or Luzern. You may find somewhere which appeals even more.

Of course, if you take a slower train for a portion of your journey, there will be even more places to visit but that may just add confusion!

Just an FYI on my experience hiring a car and driver to take my mother on a similar trip from Frankfurt airport to Basel. Normally we would have gone by train but when she arrived there was extensive work on the line and instead of a direct (no changes) train to Basel, the trip would have entailed four (!!) changes, one of which was a bus. That seemed to be too much for an 87 yo woman bringing two full size suitcases and a carry-on (don't ask). I booked the car and driver through Black Lane (one of the few options available at the time); the price was 600 euros. We were supposed to be driven in a full sized Mercedes sedan.

It was not a good experience overall. First, the Mercedes was one of those 4-door coupes which have very little back seat legroom compared to the normal Mercedes E-class sedan. Second, although we were paying quite a decent amount, the driver did not provide complimentary small bottles of water which we had expected (they cost less than 1 euro each; Black Lane said people only get those when booking an S-class Mercedes or equivalent). Next, I asked that we have a rest stop on the way down to Basel, knowing that there was a very good facility on the autobahn outside Baden-Baden (which I suggested to the driver as the best place to stop). The driver flew right by that to a very basic facility (about two steps up from porta-potties) a significant distance away. When the driver got to Basel's outskirts, he had no idea how to get to our address. Good thing I lived in the city so could give directions (even though I don't drive here).

Anyway, that was our experience so I add my voice to those suggesting a train trip instead.

!
 

Excellent advice; it looks like Lugano may be a good option1

Some suggestions:
Venice dp 13.18 - Colmar ar 21.35, change at Zurich and Basel
Venezia dp 16.18 - Gallarate ar 19.52, direct train,
Gallarate dp 7.54 - Colmar ar 12.34, change at Basel

what would be my best route if we wanted to break up the trip with an overnight in Lucerne instead of Lugano?

Venice - Milan - Lugano - Lucerne - Basel - Colmar
change at either Milan, Lugano or Arth-Goldau, plus Basel

IF you choose the Lugano option, a few recommendations
Hotel: Lugano Dante Hotel. Great location, recently renovated, wonderful staff. We stay there a few times per year -- most recent was last month, next will be in February
Restaurants: Bottegone del Vino and La Cucina di Alice

The (direct, no changes) train journey to Basel is pleasant and scenic.

if I understand correctly:
venice to Milan
change to Milan to Lucerne
stay in Lucerne
take Lucerne to Basel
change to Basel to Colmar

are those transfers fairly intuitive? In Japan, the transit system is ridiculously simple, but this would be our first experience with a European rail system.

There is one direct train Venice - Lugano - Arth-Goldau - Zurich every day.
For Lucerne you have to change either at Arth-Goldau (usually same platform or at Lugano (small station with 3 platforms only).. Lugano is a much more scenic place with scenic view to the lake and the mountains, even from the railway station restaurant.
Timetable: Venice dp 15.18 - Lugano ar 19.28 - Arth-Goldau ar 20.42; connecting trains Arth-Goldau dp 20.49 - Lucerne ar 21.21 resp. Lugano dp 20.02 - Lucerne ar 21.41

In all other cases, you will have to change trains at Milan AND Arth-Goldau or at Milan AND Lugano.Milan is a big railway station where you can easily walk 1/2 - 1 km from one train to another.

Trains Venice - Milan run about every hr. Seat reservation compulsory.
Milan - Arth-Goldau every 2 hrs. Milan dp 9.10, 11.10, 13.10, 15.10, 17.10, 19.10 with immediate connection to Lucerne at Arth-Goldau. Seat reservation compulsory
Milan - Lugano: trains every hr, Milan dp 6.43 until 20.43, Lugano ar 7.58 until 21.58.No seat reservation needed.
Direct connections from Lugano to Lucerne from the trains Milan dp 12.43, 14.43, 16.43, 18.43, 20.43. In all other cases, there will be another change at Arth-Goldau. No seat reservation needed.

A lolnger stopover at Lugano (railway station luggage lockers) is highly recommended.

Train is by far the best idea if there are no direct flights Venice/Basel. Train schedules for summer 2023 are online now at www.sbb.ch/en but you won't be able to buy tickets until much closer to the date.

You should plan to buy the Venice S.L. / Lugano ticket from Trenitalia 90 days out. www.trenitalia.com. then buy the Lugano/Basel SBB ticket either from a machine at the Lugano station on the day of travel OR on ww.sbb.ch/en 60 days out. Basel SBB to Colmar - get from a ticket machine in the Basel SBB station, French sector. NOT from a normal ticket machine in the main station hall. French sector is a very short walk from platform 1...just off the main station hall in fact. If you want to get it online you can get it on www.sncf-connect.com

Personally I would go to Luzern, not Lugano and add a night there so 2 nights not one. Lots to see and do in the area including mountains ! In which case I would take the direct Venezia S.L. to Zürich train and change at Arth Goldau for Lugano. That is usually a matter of just crossing the platform...

So, you believe two nights in Luzern would be enough to enjoy the city?

2 nights is better than 1 ! Luzern is a very pretty, very Germanic town, easily walkable. And on both a lake and a river with mountains close by. You could spend the evening of arrival walking around the old town and next day take a lake cruise over to Vitznau and go up Mt Rigi on the cog railway. Views from there are stunning (the Victorians called Rigi "The Queen of Mountains" !) Then continue with the boat to Flüelen where the scenery is like a fjord. Return to Luzern by train. Buy a Tell Pass - www.tellpass.ch - for that day and it will cover all of the above. Then for Colmar - you are about 2 1/2 hours away by train. An hour to Basel SBB station. Change to the French sector and train to Colmar - 45 or 50 mns. See www.luzern.com/en for more info on Luzern and to find available hotels. Book the hotel directly with the hotel to get the best rate...

If you come by direct train from Venice dp 15.18, 2 nights at Lucenre means 1 day.

yeah, I noticed it would get in late. Ugh

In June, there will be daylight until your arrival at Lucerne.
Both trains I mentioned (EC 310 Venice - Arth-Goldau and IC 21 Lugano - Lucerne) have dining cars.
So you can have dinner before your arrival at Lucerne.

I may need some help knowing which/where to book when it’s time. :)

additionally: I’ve made it so we can have 3 nights in Lucerne.

The Milano C - Luzern or Arth Goldau trains have dining cars too. But I don't recommend the cooking! better to eat in Luzern I think. Great that you have managed 3 days there. It is a wonderful place to be!

They will arrive at Lucerne towards 10pm.

In which case better to have dinner on the train OR stay in a hotel with room service...