Owners of houses are on public record. It would be easy to mention the mom in passing to someone. I would think the automatic reaction is, "Where? What neighborhood? Did Savannah buy her mom a nice house?" That person mentions it to someone else who Googles the address on public record, then curiously Google Maps the house. On satellite they see the house is set by itself and is secluded. There is no fence, no neighbors to see anything. They might even think, "Wow, she's off by herself. That could be dangerous." Then, that unfortunately when a plan of their own is germinated.
They are close enough to the Mexican border and the I-10 interstate freeway, where it would be easy to hide her and figure things out as they go along. What they didn't plan on was she has a heart condition and she died on them soon after they took her. That's why it took days to get a ransom note, instead of the next day. They didn't know whether to go through with getting money or to just toss her behind some big cactus out on the desert. They no longer had proof of life. That's why they described taking off her Apple watch and breaking the floodlight in the back, instead of showing the mom still alive.