Why didn't they .....

They were three hours drive away from their friends.

And if you expect people to drop everything and come running on a six-hour round trip just to do some babysitting, they will not be your friends for long.

Also, the father could have phoned his buddy Michael back and invited them to stay over like they offered, but the sleep deprivation was already taking its toll.

Hiring the babysitter was a smart move, but it turned bad when the halucination turned out to be an actual murderer.

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Blood of Thrones - proceeds to Action Cancer:
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We don't know where Penny's or Alex's families live. They could be in another part of the country. Also, Alex's parents have each been married three times. Penny refers to her mother as a "train wreck". In other words, they may not be willing or able or competent to watch baby Tanner, or else neither character is emotionally close enough to their parents to ask.

The other reply addresses the issue with friends, although, if a close friend of mine dropped all contact or sounded crazy when I talked to him, I'd make the trip a lot sooner than [friend who finally showed up] did.