I'm so sorry that your vacation was cut short by illness. It's never fun to have a sick child, or husband, and somehow being away from home makes it seem much worse.
But don't be so hard on yourself for not seeing the signs that your daughter was getting sick.....most of us don't! It's so easy for our little brains to make excuses, she was tired because of the long trip, the excitment, the time change, the weather change, whatever, lol. But that's GOOD...because otherwise every time our kids sniffled or was tired we'd be at the hospital!
I know that RIGHT NOW you're looking for symphathy, and please know that I do symphatize with your situation....so perhaps don't read this next section until you've been home a day or two and can look back on the situation a little more objectively. Ok? Because this is said with great respect and care for your situation!
I'm not sure what you expected the hotel to do for you that they didn't try to do? As much as I travel, I can't think of a single hotel where they had a doctor on site....and I've gotten sick away from home a number of times. You said that the front desk transferred you to Centra Care.....you didn't mention anything about being transferred more than once (which would be annoying)...simply that you called and asked for a doctor and they transferred you to the nearest medical facility. That's what I would expect them to do, transfer immediately to help! According to my GPS program there is a Centra Care 8.4 miles off of Disney property....I'm sure during the ride there it seemed like an eternity to arrive, but that's closer than the nearest hospital to my house! I think that if the Disney Shuttle bus driver drove you to Centra Care that is way above and beyond the call of duty...so it sounds like they were trying to do whatever they could for you and went to pretty great lengths to do it. I have had to either drive myself or call a cab! The fact that Centra Care doesn't have doctors that make house calls, well, that doesn't surprise me at all.....I don't know that there are really any house call doctors anymore. Maybe I just don't get sick in the right towns, but I have always had to drive myself to a doctor, even from 5 star hotels. And again, I know that 2 1/2 hours waiting at a medical clinic is not any fun, but that's actually a very reasonable time for a clinic to see a non-life-threatening patient. And yes, 102 degree fever seems horrible, and no one tolerates seeing their child suffer well, but 102 is not considered worrisome by the medical profession in an otherwise healthy child (not otherwise ill prior to this incident). In fact, most medical facilities would have considered your DH barfing to be the more serious of the two symptoms.
It's always, always more difficult to cope with emergenicies when you are far from home.....from where you know who to call and where to go. And it does sound like you started to panic just a bit. But, some of that may be because you're a relatively new parent it sounds like....and that's ok, we were all there once! While I hope that your daughter never gets sick on a vacation again, the truth is that it will probably happen at some point....so look at this incident as a feet to the flames lesson learned. Next time you will know a little more what to do and expect from a vacation facility (be it Disney or the 5 star resort in the middle of Manhattan). If it's a life threatening illness, you should be calling the ambulance, whether at home or away, but for the other more common illnesses you need to take a deep breath and realize that it's going to take time....and focus your energy on making your daughter comfortable and as happy as possible under the circumstances (distraction) instead of getting so upset about a short ride to a doctor or a wait in the clinic. Your home doctor may have been able to see her quicker, but I'm sure you've also had to wait at his office for what was not a pleasant amount of time as well. We all have!
As for the "have a magical day" thing....I think that is so drilled into them during training that they probably say that to their own kids when they tuck them in at night, lol. Yes, it's very annoying for someone else to be perky and cheerful when you're so worried, but please realize that they certainly didn't understand the full extent of the situation. It would be nice if people could read our minds and know our needs and somehow we want it even more from those in the service industry, but the clerk was simply trying to get your check out. I don't quite get his confusion about in or out and that would be annoying without all the other problems, but I think I can confidently say that he wasn't trying to annoy you on purpose!
Brava to you though for thinking to call the insurance company about how to get a refund.....I would never have thought of that. And it sounds like it was a good thing too, because it sounds like you needed hoops jumped through to collect. I never get
trip insurance, but now can see where it would be helpful. Of course, with just a cold I'd have probably stayed another day or two to see if the vacation could be salvaged, but you had such a strong need to be home, it was the wise choice for you!
I hope that your daughter's recovery is quick and uneventful. The coxsakievirus is pretty common and with good medical care she'll be up and running around being your honey bunny in no time at all.
I hope that you are able to give WDW another shot at making a....well I won't say it....but here's

to help you along!