I have never understood why people have such problems with separating ball joints. All that has to be remembered is that the conical part holds together with friction. (In France people don't even bother with dedicated ball joint separators.) Whether you use them or not, the first thing to do is crack the nut then undo it until it is all still on the thread but not leaving any thread open to be damaged by subsequent operations. Now give the nut a hefty thwack with a hammer. Supporting the other end on a big socket or something that will allow the other end of the threaded part to move. Sometimes that will be enough to separate them. If not, put pressure on the end of the thread/nut combination and at the same time smack the side of the joint with a hammer, cf @bluebeasty this is to distort the female cone-shaped housing just enough to free it for a fraction of a second, enough to allow the male part to slip. If that still doesn't work, and this requires a tiny bit of practice and coordination, go for "double hitting" which is where you use two hammers and hit the side of the ball joint at exactly the same time as you hit the end of the thread/nut combination. Don't forget to support the opposite end of the joint on an axle stand or some such. The whole point of all this is that it takes a relatively massive amount of force to pull the cone shaped pieces apart, but it take much less force to shock the female shape out of round to allow the other bit to move. I have heard of ones on lorries being so hard to do that mechanics undo the nuts then take the truck down a favourite bit of potholed road to shake them all about and free off the ball joint. If all else fails, go to Halfrauds and buy the one that looks like a weird set of nut crackers, I have one I occasionally use and the business part takes a 1" socket, IIRC. Good for where hammer access is difficult. An old mechanic mate of mine took one of those typical forks you hammer on the end of and welded it to a long piece of round section bar, lengthening the bit you hit, so he could split the joint from afar! More comfortable than grubbing around on the floor and hitting his fingers with his FO hammer! Just remember, the bigger the hammer, the less you have to swing it and the more control you have over things.