I am trying to remove my front axles, but the lower ball joint won't separate. What do I do?

One trick suggested by Jason Drew is to remove the lower control arm (LCA) to subrame bolt. Then remove the fork to LCA bolt. The arm should swing down and out the way.

If you can't, another suggestion by Jeremy Gilbert is to loosen the top ball joint (do not remove the nut the whole way) and tap the knucle so that it drops a little. This should give you the clearance needed to remove the axle.

If your axle is seized into the hub, it is suggested by Jafromobile to use a big hammer and a big hole punch in the center of the axle to seperate them. (there is a hole there) Penetrating oil helps. So does heating it with torches, but using a torch risks metling the plastic abs sensors.