Answer: Based on your description I am not certain what is happening to your barberries. They require a well drained soil, meaning not sopping wet or saturated, and they are very drought tolerant once established. However, as new plants they would need evenly moist soil, meaning damp like a wrung out sponge, to encourage them to root and establish. The boxwoods would also need an evenly moist yet well drained soil, so I am not certain why only the barberries are showing distress.
Over watering and under watering can both cause drooping or wilting due to root damage. Your goal in watering is to keep the soil evenly moist like a wrung out sponge, not sopping wet and not dried out. To know if you need to water, dig into the soil with your finger. If it is still damp, do not water yet. When you do water, apply it to the soil surface and water thoroughly and slowly so it soaks down to the deeper roots. After watering, wait a few hours and then dig down to see how far the water soaked in; it can be surprising.
There is no set schedule for watering, it depends on your soil type and on the weather. Using an organic mulch several inches thick over the root area will help reduce watering needs as well as feed the soil gradually as it breaks down over time.
Since these are new plants and they are defoliating, you might want to contact your county extension for help in diagnosing the problem more specifically. And, if there is a warranty involved, you may also want to check in with your retail store.
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