How should I handle a 13-month-old who hits her mother?
First of all, don't worry. It's completely normal for a child this age to feel frustrated and to show her emotions by hitting, kicking, or even biting. Remember that she doesn't yet have the verbal skills or sophistication to express herself in words.
The fact that so far she's only hit her mother doesn't mean anything beyond the fact that her mother's there when she's feeling the most frustrated (or tired or hungry or sick). She's not passing judgment on her parents.
The best thing you can do is be patient and reassuring when she's upset. Talk to her in a soothing voice. Gently stop her fists from swinging until she calms down.
When she's a bit older and becomes upset, you can help her by putting her feelings into words. ("I can see you're angry at me for telling you to go to bed.") This will help her learn to use language instead of her fists to express her overwhelming emotions. But for now, just be patient and soothing.