If you only need to work on the differential, then don't remove the hubs from the halfshafts. Instead undo the 6 bolts that go through the end of the axle housing (behind the brake backing plate), through the backing plate and into the bearing housing. You'll have to bend back the locking tabs first.
This step is required anyway to pull the diff out, and isn't any easier with the hubs off. With the 6 bolts out, you can pull the hub & halfshaft out as an assembly.
The hubs are mounted to the halfshaft with a "locking" taper (in addition to the key & nut), which tends to get very tight. Using an ordinary hub puller will almost certainly distort and ruin the hub. There is a special factory puller that supports the hub flange better and gives you at least a fighting chance of not ruining the hub. If your local club doesn't have one, and you have to separate the hubs, then my suggestion is to remove the hubs & shafts together (as above) and send them to someone who does have the puller. (Herman van den Akker and John Esposito are two.)
Note that there are other special tools involved in working on a TR3 diff ... might be easier to just find a used one locally.