Well, that's the problem right there. It's like saying you've taught Bayes to maths student, and people had no trouble with it. Now try going bayesian on the ass of someone who not only is ignorant enough to believe that homeopathy works, but WANTS to believe that, so whatever argument or counter-argument you present MUST be flawed in some way.
Same thing with going Socrates or Plato on people's ass, really. Sure, whoever was smart enough to take a philosophy class gets it. Try convincing the bible-thumping neighbour with it, though, and may Hermes be with you.
For a start, the original Euthypro dilemma involves more than one god, with different morals. So if two gods are in favour of two different things, can you say one is right and the other wrong? It doesn't work all that well in an exclusive monotheism.
No, really, I actually tried to pull that argument on a couple of believers, and the obvious (and tbh expected) way out was simply, "yeah, but our God is the right one, theirs doesn't even exist." Dilemma resolved right there.
"Ah, but how do you know your God is the right one?" you might go. Turns out most people have no problem closing the logic circle at this point. They know their religion is the right one, because their God condones the things that are moral. E.g., actual answer from a believer, "Our god doesn't tell people to fly into buildings." (Well, neither does the Quran, but hey...)
Well, ok, so instead you decide to take a more modernized version of Euthypro, and go, "But what if god did something immoral? Could you still say morals come from god?" or "How do you know that God is moral?" or some such. Well, they have an answer for that too. Namely, some version that God is by his very nature incapable of being anything but perfectly and infinitely good and moral. You get about as far with that as asking someone "how do you know a square doesn't have three sides?" It's by definition so, duh.
Essentially never underestimate how strong the force cognitive dissonance is in some people. Not only they aren't philosophy students, they don't want to have anything to do with any philosophy that contradicts their TRUTH.