Black widows are commonly nocturnal, night time active and will only bite a human if threatened. While the bite can be painfull it is rarely fatal, only 63 people have died from these spider bites since about the 1960's but whether that is because few people make contact with them or that they are simply not as large a problem as once though I can't be sure. The reason the spiders are around is because you have a good source of food so working toward eliminating that food source, insects, can help as will eliminating any place they can hide during the day.
With small children around (they are the most susceptible group for really adverse reactions) I too would want to eliminate the wee buggers, but also would be averse to spraying anything to control them. There is nothing you can spray to control them that would not have adverse healthy affects on your children, keeping in mind that anything that will kill a spider is toxic.
I spend many hours researching about Black Widows, Brown Recluse Spiders, and Rattlesnakes because I teach First Aid classes and want to know about what I teach and I am finding that in spite of everyones fear there is very little contact, by humans, with these critters.

tenderkat, I'd strongly suggest that you call a professional company to treat your crawl space and the perimeter of your home. There are products on the market that are very effective against spiders, and when used properly, pose few problems for you and your family.

Professionals have the tools required to get the job done thoroughly and safely. Email me if you want the name of one chemical that is strongly recommended for this very kind of situation.

There does not seem to be easily accessible information about how many people get bitten by the Black Widow spider, or any other spider but I am told by people that work in emergency rooms that these are not one of the, even minor, problems they see. As this information from the Universtiy of California says no one has died form a Black Widow spider bite in at least 10 years.

Here is a link that might be useful: Calpoison