I'm sorry to hear this happened.
It's hard to say for certain what the problem was.
It could have been that she was overwhelmed with the amount of kids and just couldn't lick them all dry - the most I have seen born at once have been twins and even then it is a bit if a race against time for the doe to lick them clean. To prevent this happening again you can just watch for all the signs of birth drawing near and check up on her often. Some people use baby monitors at night in the goat barn so they can hear if there is a birth happening.
She may not have allowed the two cleaned up kids to drink from her udder in time. Some does just don't really understand that they need to stay still for the kids, or the kids have trouble finding the udder. This is where I am most likely to intervene in a goat birth, as things can go downhill really quickly if the kids don't get colostrum soon after birth.
It could have been that there was something wrong with the kids, and the doe rejected them. To avoid this you can feed your does the right minerals and supplements before and during pregnancy so that the kids won't have defects due to bad nutrition.
It could just be that she isn't a very good mother. Do you know how old she is? I have seen does that were kidded when too young ignore their kids after birth.
It could also be that she was distracted by the other goats.
I agree with everything Annie said above. One thing I can add about signs of birth is just to observe each goat's normal behaviour, often they will act differently to normal when the birth is getting very close. Other signs like udder swelling, loosening of ligaments, mucus and so on can show that the birth is within the next few days, but a change in behaviour will often show that it's going to be within a few hours.
I have never heard anything before about avoiding alfalfa for does. My
dairy goats have always done really well on it, we just make sure to feed kelp as well, so that they get the iodine they need.