K.W.
I'm with Rose on this one--I lived in Texas myself for 7 years and that place is pretty buggy. It really doesn't reflect on your cousin's housekeeping, especially in an apartment where they might wander in from next door. (Down there they are commonly/politely called "waterbugs," as people do acknowledge that the critters come in regardless of precautions.)
The problem with having her bomb her apt. is that your 4-year-old will be exposed to freshly-poisoned surfaces (carpet, upholstery, etc.). To me that's scarier than a bug, and I'm an arachnophobe!
Take Rose's advice and switch the lights on when moving about at night. Keep a flashlight handy; use a nightlight. But really, I don't recall ever seeing one outside a kitchen or bath--they are looking for food and/or water, and aren't interested in the rooms that only have furniture.
One other thing--Palestine has a great little excursion steam train--a little half-hour ride through the trees--that is lots of fun. I hope you enjoy your visit!