The Korsør and Nyborg train lines are connected by the InterCity trains (and not by S-trains), and the FAQ on bikes has the following to say:
Q1. Are you required to have a ticket for your bike?
If you are travelling with DSB InterCity-, InterCityLyn-, Lyn+, or a regional train with a bike, then you must buy a bike ticket. The bike ticket covers the bike's ride and ensures that you have a place to put your bike.
It is free to take your bike with you in S-trains — they do not require a bike ticket.
Children's bikes with a frame number count as bikes and require a bike ticket. Children's bikes without a frame number (and below 30x60x100 cm) are considered to be toys and do not require a bike ticket.
Be aware: You can not bring bikes that require a large amount of space. This includes bike trailers, longjohns, cargo bikes, tandem bikes, and other large bikes. It also includes vehicles that run on petrol or other easily ignited fuel, and Segway Personal transporters / OBG Rides (electric scooters).
https://www.dsb.dk/kundeservice/kundeservice-filtre/cykler-og-barnevogne/cykler/cykler-i-fjern-og-regionaltog/
(my translation)
So it is at least not allowed when attached to the bike. There's a different FAQ item that discusses an exception to this:
Q4. Can I bring a bike trailer?
You can only bring a bike trailer if it is collapsible, the wheels have been removed, and if the dimensions do not exceed 30x60x100 cm.
Unfortunately, it does not seem like the Bob YAK trailer is collapsible or that it fits in those dimensions. So it is not allowed.
What if you try to bring it anyway?
You are only traveling a single stop, so if you board the train at a time when it is not crowded and there is plenty of space, and you wont disturb other passengers, then you will probably be allowed to bring it if you ask nicely. I would recommend detaching the trailer and standing ready at the right spot so you can enter with your bike quickly. InterCity trains stop at stations for a relatively long time, so you should have time to get both inside the train. Of course, you should buy a bike ticket, maybe even two to be on the safe side (they are only 20 DKK).
You can tell where the bike entrance will be by looking at the info screens. There will be a bike symbol on the illustration of the train:
(image source)
You will be able to tell where this is on the station, because the letters A, B, C, D, E on the bottom of the screen will correspond to signs on the station. For example, this picture shows the sign for section C on the right:
(image source)
Getting on to the platform should not be a problem as there are elevators. However, getting the bikes into the train is not as easy as there will be some steps:
(image source)
However, this kind of train stops at the station for a relatively long time, and the train does not depart until the conductor signals with a whistle. The conductor will not do that if they can see someone is still boarding the train. So if you make sure to stand ready at the right spot when the train arrives, you should have enough time to carry both pieces of your bike on board.
The picture below shows the area for storing bikes. When you enter the train, you will get into the area behind the door in the back of this picture. Once you have both halves of your bike inside the train, take them through that door and put them in the bike area. There are restraining straps for securing your bike.
(image source)
