I'm referring to the following sentence, where I've placed the topic in brackets:
（お婆は）溺愛する一人息子の又八が唆されて村を出たと思い込み、武蔵を激しく憎み命を奪うために旅を続ける。
I'm unsure as to who's actually doing the 溺愛： お婆は息子を溺愛する？それとも息子はお婆を溺愛する？
Furthermore, would it make any difference as a past tense?
溺愛した一人息子の又八が…
Japanese relative clauses can be ambiguous and both interpretations are possible.
From the context I would say it is お婆は息子を溺愛する, because she loves the son so much, she is willing to make sacrifices for him and go out in a travel of revenge.
溺愛した一人息子 seems strange because then she used to love him, but doesn't love him any more?...
Putting the sentence in the present makes it clear that she still loves him.
