My cats suddenly fight: Is it redirected aggression from outside?

I agree! What you may be seeing is redirected aggression. The angry cat couldn't get to the source of its anger (the outside animal), so it projected it onto the other cat. I would separate the cats, and slowly reintroduce them to each other. Take the cat who is aggressive, and put her in her own room with her own food, water, and litter box. Keep the door closed, and for a few days, feed them both treats on other side of door so they associate each other's smell with a good experience. Then let the other cat in the aggressive cat's room while the aggressive cat is in a cat carrier. They can smell each other, but not be in contact. If either becomes upset or show signs of aggression, remove the second cat from the room, and try again later. Praise them when they interact appropriately. When they are interacting well with each other through the carrier, you can let the aggressive cat out of her room, and see how she interacts with the other cat. Praise them when they interact appropriately, and separate them with any sign of aggression or upset. I would get a cat tree with lots of shelves to give the cats vertical space to get away from each other. I would keep the cat in her room when you go out until they are comfortable with each other. I hope this helps!