I think the crux of the problem lies in the placement of the end phrase “on the chair.”
If you would rewrite the complex sentence thus: “On the chair there was a cat whose tail was long,” it would make more sense. You could alternatively split it into 2 simple sentences: “There was a cat on the chair.” & “The tail of it (the cat) was long.”
You can also use a punctuation mark to make the meaning clear thus: “There was a cat on the chair, whose tail was long.”
The simple preposition of place “on” shows the relation between the subject “cat” and the noun object “chair.” “On the chair” is therefore not part of or does not belong to the subordinate clause “whose tail was long.” It tells the reader the cat is on the chair, the tail might also be on it, or not, or dangling from it. Therefore move the adjective phrase “on the chair” either to the front of the sentence, or close to the word “cat”.
I think you might also want to consider using a compound sentence as a last example: “The cat is on the chair and whose tail was long.”