The quality of the hay is probably more important than the type. The hay needs to be of good quality, meaning fine stemmed, leafy, and free of dust and mold. I fed my goats almost exclusively on alfalfa hay for years. Where I lived that is what was available and that is what we fed. Didn't make any difference as to whether they were bucks, does, or wethers. Every other goat person I knew in my area fed all their goats alfalfa too. People in other areas of the country feed their goats, including milkers, grass hay because that is what is available. Unless they are young growing stock, pregnant, or milking, they do not need grain.
The only case of urinary calculi I ever had was in a wether whose automatic waterer failed and he was without water for some period of time before anybody noticed and fixed the problem. Access to plenty of clean fresh water will go a long way in preventing bladder stones. Some people add a little apple cider vinegar to the water, too. I have no idea whether that helps, but it can't hurt.
There is a peppermint horse treat that goats go nuts over. I forget what it is called but if you look around the feed store you might be able to find it. To tame your goats, you might try tying them up short for a little while every day and handle them, groom them, and give them treats at that time. Be persistent. It is going to take time and it will not happen overnight.