Everything in your setup is fine. The basking temp is a little to high, only a couple degrees, but as long as he has levels to his basking spot, he can get to the temp he feels most comfortable at, having the basking temp a bit over 115F is perfectly fine.
The fact he is shedding could be why he hasn't eaten. Shedding can be uncomfortable for bearded dragons, making them go off feed. The daily soaks are a bit too much, misting several times a day should be more than enough to keep him hydrated. I suggest cutting back on the daily bathing, as this could be stressing him out and a stressed dragon doesn't eat as well. A soak once a week is more than enough with daily misting.
As he is still doing bowel movements, he isn't likely to be dehydrated or have a blockage. Not sure if you had a fecal done when you had the vet check earlier, but deffinitely something to do next vet check, to ensure he doesn't have a problem with parasites. Also, to keep down stress, avoid handling him the first couple weeks or a month or two, till he is back to eating regularly and feels comfortable. One way to notice stress is seeing alot of dark bars or splotches on his belly, normally this should be an off white with little to no markings. If his cage is in a heavy traffic area, covering up most of the viewable area (ie, if in a glass tank, the sides and part of the front can be covered with black construction paper, slowly removing them as he settles in, maybe one area per week or two. This gives them more time to adjust to all the usual comings and goings of the household.
The sight of other pets could be causing stress, other bearded dragons, lizards, cats, dogs etc.
Silkworms are a great feeder insect for bearded dragons. Though not all local petstores carry them, they can be ordered via the internet from places like www.mulberryfarms.com and other places. If you are in Canada, try www.silkworms.ca. Silkworms are more costly then crickets and other feeders, but are very healthy, have a high calcium low pospherous ratio, are high in water and protein and very easy to digest, since they have a very soft exoskeleton, being basically a catapiller. They are a little higher in fat content than say crickets, but the small difference is overweighed by the other benefits silkworms have. A variety of insects is good to offer your dragon, as no single insect is 100% complete in nutritional content, so offering crickets, superworms, a few waxworms (these are very high in fat so shouldn't be offered more than a couple a week at the most), butterworms, various species of roaches (though I understand why you can't use roaches, giving your daughter is alergic to them) and other feeder insects.
I don't remember you mentioning, but do you also dust your crickets daily with a reptile multivitamin and calcium with D3 powder? It is good to do this to ensure your dragon is getting all the nutrition he needs.
Hopefully shedding is the reason your dragon hasn't been eating much the last couple days and once he is done shedding, he will be back to eating 20-30 crickets a day and some salad.
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PHLdyPayne