Yes, that does make sense. You won't have time for everything, but you'll have some very good choices in front of you.
Auf Schönburg will cut into your sightseeing time to a degree because it's an experience in itself, and once there you will probably want to stay put. You will require a taxi ride to reach the castle - inquire with staff or mgmt. about that - and to return to the station for your 2+-hr. train ride to CGN KölnBonn Airport (that's the name of the train station to use with the DB site when you prepurchase your train ticket for June 18. Saver fares include at least one high-speed/long-distance train and are currently around €18 each that afternoon for the 3-train sequence that gets you to CGN.)
That said, FRA has an advantage for you; getting there is faster and easier - and more certain - when you travel to FRA from Oberwesel, which sends off DIRECT trains to FRA airport. The RE (regional express) is direct and gets you there in just 1 hour at €20. And because it's a regional train, that price at the station is the same and will remain the same (unlike the saver fare, which rises as tickets sell) so you do not have to pre-purchase this ticket. It is scheduled every 2 hours or so - sample departure times include 9:30, 11:30, 13:30, 15:30... Use this station name to find the train to FRA schedule at DB: Frankfurt(M) Flughafen Regionalbf
When I am headed to any airport in Europe, it's a strong priority to get to the airport easily and dependably at the time I want to get there - and from Oberwesel, this direct train option to FRA would be my choice. You can also find connecting train options to FRA at the DB site with saver fares (priced at €18 each) but I would avoid those. They always include long-distance IC/ICE trains (which are not as reliably on time as the regional trains tend to be) and you always have to change trains (so you must fuss with your bags, possibly in a rush - and must rely on additional trains for timeliness.)
On Google flights I am seeing three pm Lufthansa flight options priced at $74 for FRA - VCE vs Eurowings $62 for CGN - VCE. I haven't flown Eurowings but I think the ground transport time and other issues with reaching CGN - and my good experiences with Lufthansa - would encourage me to opt for FRA.