Two Different Toyokuni IIs
An additional complexity is the fact that there are two different artists who are sometimes referred to as Toyokuni II; and similarly for the later-numbered artists called 'Toyokuni'.
The first Toyokuni II was Toyoshige, a mediocre pupil and son-in-law of Toyokuni I who became head of the Utagawa school after Toyokuni I died.
Kunisada I (Toyokuni III) apparently despised Toyoshige, and refused to acknowledge him as head of the Utagawa school. Apparently, this was because he felt that as the best pupil, he should have been named head after the old master died, and was upset with Toyoshige, who apparently got the position because of his family connection.
When Kunisada I took the art-name Toyokuni (c. 1842), he effectively removed Toyokuni II from house history and for a period actually signed as Toyokuni II. However, he is now numbered, Toyokuni III. There are prints which signed Toyokuni II which are by the artist now known as Toyokuni III.
This numbering persisted, so when Kochoro became head of the Utagawa school, he signed as Toyokuni III, although by he would be the fourth Toyokuni. Likewise Kochoro II eventually signed as Toyokuni IV, and is now numbered Toyokuni V.
Read more about this topic: Utagawa School