One day Rhein River trip

Train to Rüdesheim and choose one of the trips offered by KD.

The cruise takes roughly 2 hours without stopovers. So with maybe half a day's time on the 15th, a full day on the 16th, and the morning of the 17th to play with, the big question is what ELSE you'd like to do on the Rhine. Have you looked at the options in the Upper Middle Rhine Valley (the part south of Koblenz where the best cruises are)? You could also be touring a medieval castle (Marksburg Castle in Braubach) or wandering around some old-world towns (like Braubach, or Bacharach, or Oberwesel) or combining some chairlift/gondola rides and hiking trails to take in the natural scenery. Or it could be checking out the big Wine Festival in St. Goar, which takes place that whole weekend, with a big "Rhine in Flames" fireworks show on Saturday night at 21:00.

https://www.rlp-tourismus.com/en/events/wine-festivals/event/20230916/Rhein-in-Flammen-Das-Original-Die-Nacht-der5/event.html

St. Goar is an ideal place for two nights if you plan to visit other places and take a cruise. You can get there by train from FRA airport in about 1.25 hours, pretty close to the same time as you'd have getting to Rüdesheim, and St. Goar is a great place to end a cruise (nearly all scheduled cruises end there. Boppard, just to the north, could work well for you as well. But I would expect heavy demand for rooms in all the Rhine towns. See what you can find and make your plans around that result.

What Mark said. Train leaving Frankfurt every hour, going to Rüdesheim. Ride the K-D ship to St. Goar. Show your train ticket for a 20% discount. The train and ship times do not match up, so you have time to explore Rüdesheim for a bit. In St. Goar, visit Burg Rheinfels, the largest, most massive castle on the Rhein. Though bombed by the French, it is still impressive and you can spend a couple of hours wandering around. The views are spectacular. Have lunch on the terrace. Visit the St. Goar church next to the train station. It is gorgeous and newly renovated. Train back to Frankfurt. Stop off in Bacharach if you have time.

"I will arrive in Frankfurt on the 15th..."

If this means you will be arriving and staying in Frankfurt proper on the nights of the 15th 16th, the instructions from Jo and MarkK are what you are probably looking for - a day trip out and back from the city.

I assumed your arrival takes place at FRA Airport (Frankfurt Flughafen on the map below) and that you are looking for day-cruise and other options on the scenic part of the Rhine Valley as you make your way from FRA Airport to Duisburg over your 2 free days.

Either way, this rail map should be helpful. Zoom in just right of center for a detailed look at the area of the Rhine that is under discussion here. Duisburg can be reached by train from ANY of the Rhine towns mentioned (Rüdesheim, St. Goar, etc.) using the railways shown.