It is imperative she eat a large snack when she comes home from school. Even on the way home she could eat some cheese crackers or PB on crackers. Yes, the car will suffer the consequences but she must have some good nutritious food in her tummy right away.
BUT
1. check with the school. Write down her eating schedule with them, regardless of how much she eats you need to know the schedule of when she is being offered food.
2. check with the child care teachers. Write down when they offer the kids food. She may not be getting a snack on some days due to the time she arrives and or leaves.
The reason I say this is because sometimes in child care and in schools it is not thought about. Some kids come in and haven't had a good lunch and then they might have orange halves with water for snack in child care. Of course that meets standards for a snack but it is not enough to tide a child over until 6 or 7 pm when they finally get dinner.
The government food pyramid takes all foods by the servings so if they have a fruit at snack they don't have fruit for part of their other meals for instance.
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This is what a typical schedule for kids is supposed to look like. (according to state child care guidelines, they include this in them so that child care workers can understand the full day for the kids and incorporate their menus to reflect what they think kids are getting at home and school).
Breakfast:
Grains (Oatmeal, pancakes, toast, biscuit, cereal), fruit (1/4-1/2 cup 100% juice or 1/4-1/2 cup fruit like a banana), 6-8oz. 2% milk, protein (does not need to be a meat).
Morning snack:
Juice or milk and then something yummy and fun. Counts in the food pyramid and should not totally be in the tiny part...lol.
Lunch:
Main dish, something like spaghetti O's is good since it has 1/4-1/2 cup of veggies in it. My granddaughter was reading the can the other day and noticed the new big print...she said "I've been eating vegetables?". I reminded her that tomatoes were vegetables so she was satisfied. But kids will eat stuff like this and other pasta dishes without realizing they are eating veggies too.
A sweet fruit like strawberries or grapes is a good choice. They don't make horrible messes and are easy to bite and toss stems and leaves away.
Jello, bread, carrot sticks with ranch dip if you have a little container, all kinds of foods can go here, only you know what she likes or dislikes.
Afternoon snack:
This usually happens after kids wake up from their naps and big kids come in from school. They use more energy sleeping than when they are awake. They need almost an instant feeding.
This snack time is important for a couple of reasons. They kids ate lunch at school before noon, it has been 3-4 hours since they ate, if they ate, and they are not going to get food for several more hours. They need the afternoon snack to be almost a small meal.
Then dinner should round out the rest of the food pyramid but be sure to count in the bedtime snack. Kids sleep better and deeper if they have something about 1/2 hour before they lay down. Our kids often do PB sandwiches or half of a banana with milk. Sometimes it might even be a bowl of cereal.
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She sounds tired, that cannot be fixed. She is hungry, you have the option to fix that.
I would have something in the car for her to nibble on while you travel to your house. Then I would have something with lots of protein and some complex carbohydrates for her to sit down and eat. Once she gets her tummy full she is going to be happier....hopefully????
Letting her play in the tub is a cool alternative to swimming. I let the kids all get in and play, with swimsuits on so they are modest. I think if you think about different options she may be happier too. She is used to being mentally occupied during the days when she is in school and child care and she is mentally bored without that direct scheduling. I think maybe letting her go after school every day might be a good idea.