The concern being expressed about the lack of clothing available from the Dad's house for the bloodhounds to use in the initial search for Dylan, where clothing had to be brought in from the Mom's house, can be explained, or fit into the known facts in the following way.
We know Dylan's phone, hat, backpack and cell phone charger are all missing. It's the cell phone charger that doesn't make sense, why did Dylan take that with him when he left Dad's house ? Suppose Dylan faked being asleep, or too tired, that morning to go with his Dad shopping. Instead Dylan planned all along to "take off" as soon as Dad left on the shopping trip. Keep in mind his Dad had already shut down Dylan's initial scheme of spending the night at his friends home, which can be viewed as an attempt by Dylan to get around this visit. As soon as his Dad leaves early that morning, Dylan packs up all of his stuff in his backpack and leaves Dad's house on his own with no intention of returning.