There is another part you need that is missing. I can take a pic and post it for ya. The other short brake arm has a small "dot" that you need to line up with another "dot" that is on the hub mount. It won't fit any other way, do NOT force it more than mere tapping. I'll be right back. The piece you are missing is cheap and easy to find.
Thats what it should look like. That wide black brace strap hanging in your pic should bolt to the brake hub assembly on that big "dog Ear" hanging down. Then you should have a THREADED .25" rod with a spring on the rear end that attatches to that short, about 4" or so bent metal arm that ataches to that splined stud onthe outside of the hub with the very small "dot" marking that aligns the armature which engages your brake pads. The other end goes along the swing arm to your rear brake pedal look along the top of this pic here:
It attatches just left of the return spring thatis in that pic. Here's another pic of the set-up from behind:
Just so you'll know. The dots on the cam and brake arm are to assure that the brake arm is in the right position on the cam in relation to the leverage it applies to the flats of the cam.
You can install a brake arm with the dots offset..the reason it often appears impossible is because it's been in the correct location for so long. The splines are symetrical so it you clean them good it will go on any way you want. I've often offset the dots a spline or two on a rear brake to make up for an extended swingarm or some other change in rear suspension geometry.
You DON'T want to do that to a front brake though...because it does screw up the leverage ratio.....not such a big deal on a rear brake on a race bike, or a street bike with a big long pedal.
Rat....ohhh...ok, different story then. You are saying the splines are either too course or too fine.
The hub looks like a late 60's to early 70's type....going by the riveted pivot posts.
Should be an easy part to find.