This one is pretty complex.
ni- - this prefix can refer to a specific action as opposed to a generality. It is used with the verb ᎠᏛᏁᎭ "doing" to refer to a specific action. Ex: ᎦᏙ ᎭᏛᏁᎭ? "What are you doing" vs ᎦᏙ ᎿᏛᏁᎭ? "What is it that you're doing.
-gvw- - "ga-" since - appears as gvw- in third person forms. (See D.Feeling "Cherokee English Dictionary" 1975, p. 255-256. "A peculiarity of the third person form of ga- is that the pronoun prefix u-, which normally occurs in non-progressive past tense forms, changes to -a- following gvw-.")
-uni- - "they -> it" , this is an "B" Class bound pronoun.
-akil- - habitual/progressive verb stem for "to be on something, to sit on something (a horse, a fence post, etc.)" see also - "ᎤᎩᎳ ukila".
-e'i- - non-experienced (reportative) past tense suffix. In conversation or when followed by a suffix, the "i" is often dropped.
-gwu- - suffix meaning "just"
-hno - suffix with several meanings. Can be translated here as "and so" ᏂᎬᏩᎾᎩᎴᏊᏃ - "and so they just stayed on it". Or a better sense is "and so they just kept on riding it"