Even with the comma, the grammar fails the test of consistency. Once you start with a structure you should continue with the same; in this instance, prepositional phrases: inspiration "in cooking", [inspiration implied] "from her family" and [inspiration implied again] "from her dog."
Excuse the pedantry if it offends, especially Americans.
Rachael Ray finds inspiration in cooking: her family and her dog. Big difference.
A panda bear walks into a Starbucks, grabs a bagel, eats it, then with a disgruntled look on his face he pulls out his "open carry" handgun shoots a hole in the ceiling, and walks to the door. When a patron stopped him to ask what he was doing he said nothing but pulled out a copy of a wild life guide with a dogeared page marked "Panda: eats shoots and leaves"
A comma would do the trick as well, adding a "for" changes the sentence. "Rachael Ray finds inspiration in cooking, her family and her dog" or "Rachael Ray finds inspiration in cooking for her family and her dog"
Embarrassment to tails... Someone got paid and they can't even write. But then again, someone also approved it, and they got paid even more. Not sure what's worse, but I have OCD regarding improper use of grammar and punctuation.