First, I think しないでほしい is usually not used with ～に though ”してほしくない” is often used with ～に.
しないでほしい is usually used solely. The object is "you", and it is usually omitted.
そこに座らないでほしい。 I want you not to sit there.
AにBしないでほしい can be used with "と言った", "と思った" and so on in a sentence like this:
私は彼にもうこれ以上罪を侵さないでほしいと言った。
I said to him that I wanted him not to commit sin anymore.
or
I said to him "I want you not to commit sin anymore.".
Or, AにBしないでほしい is used as another meaning like this.
彼に迷惑行為をしないでほしい。 I want you not to do him anything he doesn't like.
彼女に近づくことはしないでしい。/彼女に近づかないでほしい。 I want you not to be close to her.
In this example, The object is "you" and "someone/something".
It is the case we want "you" not to do something to "someone/something".
If you said
そもそも合気道の達人に、一般人と8時間も組み手をしないでほしい。
This means...
In the first place, I want you not to do Kumite against 達人 (cooperating) with ordinary people for 8 hours.
This is way off.
Having said that, Most people understand the correct meaning from the context.
In this sentence, 遊 talks to 先輩 directly though she? is not there.
In the first place, I want you not to do anything like that 達人 (like you) does sparring/Kumite with ordinary people (like me) for 8 hours.”
そもそも合気道の達人が一般人と8時間も組み手をするなんてこと、しないでほしい。
先輩 ＝ 達人 in this case, and I think 遊 wants to emphasize that it is too strange for 達人 to do Kumite with ordinary people like him.