I was raised with creepy crawlies (my dad bred snakes, lizards, and we had pet tarantulas). I don't mind the big ol' hairy spiders, its the teeny tiny house spiders that give me the creeps.
Anyway, as far as I know, tarantulas cannot cause any serious injury to people or larger animals (meaning larger than a mouse or tiny bird). They are venomous, but their venom is not strong enough to affect you, or your cats or dogs, and even if it was, it would only be temporary.
The biggest danger would just be the urticating hairs on the back of their legs that they "throw" at attackers in close range. They are very, very, very itchy and painful (but not medically threatening), and bound to end up in your cats' and dogs' noses. They can also bite, and while this is painful, its usually a last resort after the hairs, and I'm guessing that your little ones won't want to continue to pursue a tarantula after it has already thrown its hairs.
You can check with your vet, because I'm sure he gets calls about this a lot, and he's more familiar with the local varieties of tarantula, but there's really no serious threat.
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