There's lots of things going on in your question, so here goes:
Check engine light on: a check engine light means the onboard computer has detected a problem with something and would love to tell you about it. Who knows, maybe the computer knew about the defective cooling fan switch. Most parts stores will read these codes for free.
Overheating causing blown head gasket: as indicated in other answers, severe and prolonged overheating can cause the engine block to warp, meaning your head gasket won't seal properly anymore. If this is the case, the real issue is not the leaking gasket, it's the warped engine block. It needs to get machined or replaced, either option is a major expense.
Did the vehicle overheat by enough and for long enough to cause this? Nobody here can tell, because nobody here was there. Ask your daughter how high the temperature gauge went and for how long. Most engines have an auto-shutoff if the temperature goes too high for too long in order to prevent engine damage like this. Likely, the head gasket just blew all by itself from 17 years of wear and tear.
Is the shop responsible: well, sounds like they just threw some new fans on there without checking. It is most likely that your old fans were still working and it was just the fan switch that was defective all along. Too many shops don't perform a proper troubleshooting and just guess at what's wrong and throw parts at the car. That's why most of us on here do our maintenance ourselves.
You are welcome to go down there and shout at them and ask for a refund, but don't expect anything good to happen, and certainly don't let them touch your vehicle once they know you are upset with them. They can just as easily disconnect a hose or two to cause you to break down again. I've seen it happen.
What do you do: take ownership of your vehicle maintenance. That means when the check engine light comes on, go get the codes read for free at a parts store, even if you are not going to do the repair yourself. It's the only way to really know what the computer was saying before your mechanic got his or her hands on it.
If a shop is doing the work, ask for your old parts back. In your present case, how can you tell your old cooling fans were not the problem? They're in the garbage and long gone.
Learn how to do some simple repairs and simple diagnostics yourself. Most tools needed are simple: screwdrivers, wrenches and sockets with ratchets. Most can be had for cheap when on sale at hardware stores, online or at pawn shops. Start with learning how to change light bulbs. Except for headlights, car bulbs cost about $1 but shops charge about $30 for the labour. You'd be surprised how little a head gasket actually costs (just for the part). If you'll humor me, go to a car parts store and get a quote for your head gasket. Feel free to peruse local classifieds for a "home mechanic," they will often do the job for a lot cheaper than a shop. Some of them will go buy the parts for you and add the cost to their bill, others will let you go buy the parts and bring them with the car.