There are two corrections.
1)
It's romaji, not roma
nji ("n" is unnecessary).
2)
It's はな
やなぎりゅう, not はな
ゃなぎりゅう (や is the normal size one, not small one).
Hanayanagi is the name of a school (of dancing). This is a proper noun, so it's not translated like "flower-willow". (The meaning is indeed flower willow, though.)
Iemoto is a single word, meaning "the head of a school", thus, もとはなやなぎりゅういえもとのこ (元花柳流家元の子) means "child of a former head of Hanayanagi school".
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「家元」は英語でどう表現する?【単語】the head family of a school...【例文】She is the present iemoto....【その他の表現】the head of a school... - 1000万語以上収録!英訳・英文・英単語の使い分けならWeblio英和・和英辞書