If you burn out the remains of the old handle, taking the rivet out is pretty easy. Fitting a new handle is tedious but an hour with a small plane (a block plane) is enough to get the new one to fit. If you get it roughly to shape and then try pushing it in, rust marks on the wood will show you where to take wood off with the plane so it becomes a fairly 'scientific' process to get a good fit.
I generally use a large nail to form the new rivet. Drill through the assembled fork/spade and handle with a drill the correct diameter for the nail to fit. Don't drill bigger than you need to as this weakens the handle. push in the nail and saw it off about 4-5mm beyond the shank of the fork to have enough metal to form the rivet. Use the ball end of an engineer's hammer to gently tap down the cut end of the nail to pull the sides of the fork shank together tightly onto the new handle. Don't hammer too hard or the new rivet will just bend in the middle and make a weak joint. You can use the face of a sledge or lump hammer as an anvil.
When you have formed a tight joint, excess metal can be filed off to leave a smooth surface so your hand doesn't catch on any rough metal.
If the top of the shank of the fork doesn't form a smooth joint with the new handle, I use some car body filler to smooth over the joint. This is the polyester filler you mix with a catalyst which then sets in about 15 minutes. The filler can be filed or sanded smooth. Some brands of filler are hard and durable and some crumble quite quickly. Sorry I can't be more specific. I have thought of using Epoxy glue but it is more expensive and tends to run out if not held in place before it sets.
As far as the new handle is concerned, I coat mine with boiled linseed oil a couple of times during the summer. This seals the wood and gives it a nice smooth hard finish. I do the same on all wooden handles of equipment I use outside (rakes, shears, hammers, etc.). A small bottle of oil from the local paint shop lasts forever so it's a cheap way of keeping the handles in good shape.
Another trick is to have an old bucket of sand into which you pour old engine oil. When you finish working with a fork, spade, shears etc. remove any mud and then push the metal end into the sand. This oils the surface and the sand gives it a slight polish. I stay clean and shiny ready for when you next need it.
If you regularly break fork handles, you may be trying too hard. Give yourself and the fork and break and dig smaller sods (can I say that here?).