I think this is David Drake's Lord of the Isles series. The first book was published in 1997 so it fits the time you remember reading it.
The female character you remember is Ilna, and the scene with the spiders is in the fourth book Mistress of the Catacombs. This also mentions the cords that Ilna manipulates to do magic:
Ilna stood because it seemed undignified to die lying down. A silver-and-black spider the size of a bull had left its web and was walking toward her on legs as thick as Ilna's own. The tree which anchored one side of the structure of wrist-thick silk was a hundred and fifty feet high, but it swayed to be free of the
spider's weight. Her steps had a mincing precision like those of a crab underwater.
Ilna took out her hank of cords. It was her pride that she could control any living creature which had eyes to read her patterns; were this spider alone, she could hold it till sundown. It wasn't alone. The valley held more of the creatures than there were people in a Valles tenement. The smallest of them was as big as a dog, and even without poison their fangs could tear her apart. This wasn't the way Ilna would have chosen to die. She smiled coldly. Well, that was all right; she
hadn't chosen it.
Greetings and honour, Ilna Os-Kenset, said a voice in her mind. We to whom weaving is life bow to you, who are a greater weaver yet.
She fears us, said another mental voice. She has no reason to fear. We are her friends and her disciples.
We are your friends and disciples, Ilna, agreed a chorus, each tone different but the thoughts all the same.
"You're the spiders," Ilna said. Her gut didn't believe it, but she kept her voice flat because her intellect knew beyond a doubt that she was right.