Borders of Vassal Kingdom of Rohan

The Vassal Kingdom of Rohan:

The first part of not on the vassal Kingdom of Rohan is that I refer to it as a vassal, I do this instead of counting it amount the independent protectorats due to how Rohan go it's lands and in that the Oath of Eorl also known as the Oath of Cirion. In this oath the two kingdoms of Gondor and Rohan state that the province of Calenardhon would be forever Rohan giving it its borders and that there would be an alliance between the kingdoms.

Hear now all peoples who bow not to the Shadow in the East, by the gift of the Lord of Mundburg we will come to dwell in the land that he names Calenardhon, and therefore I vow in my own name and on behalf of the Éothéod of the North that between us and the Great People of the West there shall be friendship for ever: their enemies shall be our enemies, their need shall be our need, and whatsoever evil, or threat, or assault may come upon them we will aid them to the utmost end of our strength. This vow shall descend to my heirs, all such as may come after me in our new land, and let them keep it in faith unbroken, lest the Shadow fall upon them and they become accursed.

—Eorl

Vanda sina termaruva Elenna-nóreo alcar enyalien ar Elendil Vorondo voronwë. Nai tiruvantes i hárar mahalmassen mi Númen ar i Eru i or ilyë mahalmar eä tennoio.

—Cirion

"This oath shall stand in memory of the glory of the Land of the Star, and of the faith of Elendil the Faithful, in the keeping of those who sit upon the thrones of the West and of the One who is above all thrones for ever."

-Cirion Translation

The definition of a vassal is a holder of land by feudal tenure on conditions of homage and allegiance, of which the relation formed by the Oath fits quite well as the lands of Calenardhon were given to Rohan in exchange for allegiance. This is also why I include them in the Reunited Kingdom map as they fall under the King of the West who is the High King of the Reunited Kingdom. 

As for the borders of Rohan are very well defined by Tolkien, its borders are the river Isen from its junction with the river Adorn, with the Adorn marking the south west border with Drúwaith Iaur and the river Isen marking its north western border with Enedwaith. It then follows the river Isen northwards to the outer walls of Isengard, and from the outer walls of Isengard it goes northeast along the eaves of Fangorn Forest to the river Limlight in the north. They then follow the river Anduin and the west-cliff of the Emyn Muil, down to the of the mouths of the Entwash and then following the Mering stream. The last part of the borders of Rohan follow along the North side of the white mountains till coming back around to the border with Drúwaith Iaur on the Adorn river. As you can see here in this picture from tolkien.gr on the Horse-Lords of Rohan it follows the same path as Tolkien describes and the same is depicted on my map as well for the shape of Rohan.

This then ends the section on Rohan as there is not much else to say Tolkein was very precise on the layout of Rohan using many clear natural land references for the borders of the vassal kingdom.