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I didn't try but if I remember well it says in the tooltip that oldtown, the arbor, the Florent and Tarly duchy become the demesne.
 
They're OP. Should there not be a way to cut their realm up? Or, like in the actual books/show, have them consist mostly of light infantry and such?

Where does it say in the books that the Reach troops are mostly light infantry? If memory serves, they have more heavy horse than any other kingdom. Randyll Tarly's forces also seemed to have a lot of heavy infantry.
To be fair, none of the Regions actually have the numbers that they should- the North should be able to raise up to 55,000, the West 55-60,000, the Riverlands 50,000ish, the Vale 45,000ish, the Stormlands 35,000 (with only about 5000 at most heavy horse), Crownlands 15-20,000, the Dornish 25,000, and the Iron Islands 20,000.
The Reach itself could raise 80,000- 10,000 (although the higher number is unlikely, as Reach vassals are notoriously independent compared to other Regions).
Essentially, when Robb was faced by the Lannister/Tyrell alliance, he was facing a force of 180,000 (at most) against his own 105,000, with about 35,000ish in the North, and the Riverlords mostly with their own forces in their own keeps.