The spider didn't explode. The babies didn't scurry out of their dying mother.
Wolf spiders carry their young around on their backs. The babies had already hatched and were just hitching a ride on the Mommy Spider Taxi. Wolf spiders are actually pretty good caretakers of their young that way, and are usually one spider you -want- to have around.
A better solution would have been a vacuum cleaner. Or better yet, a glass and an index card to catch it and put it outside, where the spider - and its babies - belong.
---
Camel spiders are freaking awesome coolness, btw. They're incredibly common in the desert south-west, and they're one of my favorite arachnids (they're NOT a true spider, though). They're totally non-venomous, have the attitude of a pissed-off honey badger, and they eat anything they can catch, including scorpions, black widows, and brown recluses.
And yes, when they flare all four mandibles at you in a threat display, it's kinda creepy and freakish.