It is difficult to determine the cause of the rashes on your child's legs, feet, hands, arms, and mouth. It could be related to recent vacation activities or common childhood illnesses. I recommend monitoring the situation for now. Apply a fragrance-free moisturizing cream as needed throughout the day and keep an eye on your child's overall condition. If the rashes persist for more than a week without improvement or if other symptoms like fever appear, it would be wise to seek medical advice. In the meantime, if you have any further questions, feel free to ask.