I had this problem. Brown and black widow spiders nesting in just about every single corner of the pool screenhouse. Spiders, eggs, everything. It was really a problem. I was scared to go out by my pool. Get your garden hose with a good high pressure nozzle on it. Hop into the pool so you are safe from the spiders and go around hosing them to death, LOL. Hose them really hard and make sure they are dead, hosing away their eggs and everything. You'll have to keep doing this basically on a daily basis to keep up with it, but eventually they will all be gone.
Also be sure to eliminate the insects they like to feed on so they avoid your pool area all together.