Now am thinking we will do our first night somewhere near Frankfurt
I've been thinking about your plan, and I think that you should spend the first night, or maybe two, in Bacharach. Bacharach would certainly give them a nice German experience and the opportunity to recover in a nice setting. Bacharach is only about an hour from FRA, and every two hours there is a direct (no change), 57 minute connection. You could stop on the way in Bingen and take the KD boat from there to Bacharach, or you could go directly to Bacharach and do a Rhein cruise the next day.
BTW, I did exactly this in fall of 2017. I went to St. Goar for two nights, did a Rhein cruise the next day, then went to a small town near Füssen the third day using a train specific Saving Fare ticket when I knew I could make the train.
Another thought was to go the first day to Lohr am Main, a small town on the Main river, in the heart of the Spessart, about a half hour from Würzburg. There is nothing all that significant about Lohr, but it is a very pleasant town with a pedestrian only main street lined with Fachwerk buildings and shops. A nice place to recover from jetlag. Lohr is just over an hour and a half from FRA using the S-Bahn to Frankfurt Hbf and the hourly RE to Würzburg. What's more, it's in the direction you want to go, only 2 hours from Rothenburg, and it's in Bavaria, so you can use a Bayern-Ticket to get to Rothenburg or on to other parts of Bavaria.
I would recommend staying here. We didn't; we stayed in a nearby apartment, but we ate a Küferstube one night, and the food was excellent. It's about a ½ mile walk (1.1 km) from the Bahnhof, but there is a bus from Bahnhof Nord (opposite side of the tracks, through the tunnel from the station) that goes right by Küferstube. From the stube, it's about 4/10 mile walk to the pedestrian main street in town.