You have a DB app, you really don't switch trains, you switch tickets. So per the original plan, you buy both a VRM Minigruppenkarte and a VRS Level 5 TagesTicket 5-Personen and load them on your smart phone. If the conductor comes by between Koblenz and Remagen, you show him/her the VRM ticket, if from Remagen to Cologne, you show the VRS ticket. Same going back.
Now you are looking at changing the plan and go on a Saturday early, then turn around and go to Frankfurt airport. are you staying at a local hotel overnight, then flying out the next morning?
Seems like 137.70 EUR to take the ICE Sprinter to save 2 hours is strange given all the calculations to get to Cologne from Koblenz for the least amount of money. That ICE price is for a nonrefundable train specific ticket.
You could maintain flexibility buy just buying a Schoenes Wochenende ticket for 62 EUR, then a VRS Level 1b TagesTicket 5-Personen for 13.10 EUR to get around on local transit. You'd go to Frankfurt airport the way you came to Koblenz, then to Frankfurt airport. Longer, but more scenic than the Sprinter, although you do get watch the speedometer screen in the carriage hit 350 kph.
Its your money and your time. Take your pick.