I would offer two options:
…capitula a primo (usque) ad decimum…
…chapters from the first one (all the way) to the tenth…
…a primo capitulo (usque) ad decimum…
…from the first chapter one (all the way) to the tenth…
I would not repeat the word capitulum twice unless I wanted more emphasis.
Perhaps the second one is more idiomatic, but the first one is clear, too.
(It has an implicit capitulum which is easy enough for the reader to supply in the correct form.)
The first one has the benefit that the word capitula has a clear case and the grammatical role is more transparent; it's a matter of choosing between a noun phrase and an adverbial phrase.
When using usque to express the length of a range, Lewis and Short indicate that you should use a preposition.
To be honest, I had hard time parsing the bold part of your sentence.
If nothing else, prepositions make the the range clearer.
Notice that you can leave usque out if you will, just as you can drop "all the way" in English.
It is a matter of tone and emphasis.
Making prima and decima plural sounds fishy; there are several chapters but only one first and one tenth.
You could say capitula primum et decimum for "the first and tenth chapters", which does not explicitly indicate a range.
It is also correct to say capitulum primum et decimum.
See this question for further details.
The agreement of a noun with several adjectives makes it reasonable, to me at least, to use capitula a primo ad decimum without repeating capitulum in the relevant case after the prepositions.
It is clear what the numerals refer to, so I would consider it clumsy and unnecessary to repeat the noun.
There is a somewhat similar range expression in Ab Urbe condita 31.1:
…tres et sexaginta annos—tot enim sunt a primo Punico ad secundum bellum finitum…
I will look for more range examples, but I hope this makes my a primo ad decimum more plausible.