Hm. The dutch oven thing is new to me. So is the egg/buttermilk mixture. We don't use eggs, baking powder, or baking soda. Just pure buttermilk (or even sometimes regular milk in a pinch.) This is simple, Texas, chuckwagon cooking. Nothing fancy. Just good grub.
Season the flour how you prefer. Salt, black pepper, and cayenne is the usual. Dredge the cube steak in the flour and shake off the excess. You don't want a thick layer of flour, just enough to coat lightly. You should still be able to see the texture of the cube steak and maybe some red. Dredge it in the buttermilk and shake off excess. Finally, back into the flour one last time. You don't want to have too much coating. The star is the meat.
Use a cast iron skillet with about a 1/4 inch of oil. I'm thinking perhaps your oil wasn't hot enough, which made the batter disperse. Make sure it does get up to the 360-375 range. Also, make sure your cube steak is room temperature before you start. A cold steak in hot oil is not a good thing. Drop the steaks into the oil and cook until crispy brown. No need to put it in the oven, in my opinion. The only reason to do that would be to keep them warm. Just put them on a rack or plate with paper towel to suck out the extra grease.
Gravy
That is the weirdest country gravy recipe I have ever seen. All you need is about 5 or 6 tbsp butter and/or oil in a pot on medium heat. Gradually whisk in flour, slowly cooking it until you have a golden brown pasty but smooth rue. The key is to keep whisking constantly as you add so it does not get lumpy. Immediately start slowly adding milk until it is a golden/white color and you have the consistency you desire. The gravy will thicken as it keeps cooking. Add spices as you desire. Salt and pepper (lots of pepper) are the norm. My dad puts something in his gravy that I can't figure out and he won't tell me, but it's fantastic. It's just kind of your thing to play with as far as spices go.
Good luck! Practice practice practice.