Spiders are no joke. I am myself recovering from a bite from what was likely a common house spider here in NY. Everything I read says the best way to get rid of them is Cleaning(vacum etc), and making sure there is no food source for them, so anything that will deter other insects is helpful, rose germanium, citronella etc.
You could try some Devic communication with the spider Deva and try to cut a deal, like give them a place they can be.
I have also read that spider are attracted to places where there is an imbalance in the earth energy of a place. A Dowser may be consulted on this if you have lots of them. They may do what is essentially "earth Acupuncture" to heal the imbalance.

maybe try to explain spiders better to your children...?
encourage the large house spiders, since they prey upon other bitey spiders and don't bite people
spiders scent mark their territory, so if you just move them, they will come back to "their" spot
pet gecko? lizard? insect-catching cat?

I am hesitant to say "encourage large spiders". I saw this really cool big long-legged brown spider in an apartment I was renting and left it alone because I liked it. It wasn't a wolf spider or a daddy long-legs, I'd never seen one before. One day I saw it on the floor and tried to pick it up with a sheet of paper because there were people coming to see the apartment and I didn't want it to get killed. It ran and hid and foldedIitself way way into a tiny crevice where I could not retrieve it. About 6 weeks after I moved I was surfing around and realized that had been a brown recluse spider. I was very very lucky. I recently saw the worse spider bite I've ever seen on a local woman, it was 4-6" long, pink and robin's egg-blue, hot and raised.. She never even saw the spider. I have always kind of liked spiders and had a live and let live attitude with them. After these experiences I am changing my mind and if I had children I would also be very concerned. I don't mean to scare anybody I just wanted to relate this, please realize even in a place like New England it does happen.

Just in case, identify Plantain (Plantago major or Plantago lanceolata - do a google image search) so you can pick some from the yard, chew it up, and place onto a bite if you get one. You can also eat it or drink it in a tea (the dried doesn't work as well, but you can make a tincture with it in vodka for later storage). In your tea, I would also add echinacea and yarrow and drink it until you feel bloated!

Plantain is also good for dog bites, snake bites, and poison oak/ivy. It is best when the person who has the bite is the one chewing the Plantain before placing it on the bite. This herb has some of the best drawing properties around.