Howdy
As mentioned, these revolvers had a pin near the bottom of the grip frame to position the grips. You can see the pin down near the bottom of the grip frame in this photo, and the matching holes in the grips. You can also see that the strain screw is screwed in all the way. It is tensioning the main spring exactly as it is supposed to do.
Don't reach for that kitchen knife yet. First, try this standard method of removing the grips. Unscrew the grip screw all the way, then screw it back in one turn. The screw head should be standing proud of the left grip. Gently tap the head of the screw with a light brass hammer to push the opposite grip up. If the threaded ferule in the opposite grip starts to rise up out of the grip, stop and reach for the kitchen knife. But if you can drive a grip up this way, you can reach a fingernail underneath it to pull it up. Then you can gently push the other grip off from the inside.
Here is what the mechanism under the side plate looks like. These guns had two separate sears. The claw like looking thing in front of the hammer was called the Front Sear. This is what operated the gun in double action mode.
The single action sear was called the Rear Sear. In this photo, the hammer is cocked, and the rear sear is holding the hammer in the full cock position. You cannot see the rear sear because it is hidden down under the edge of the frame.
I tilted the camera down for these next two shots so you could see the Rear Sear. In this view the Rear Sear is the part below the hammer holding the hammer back slightly in the 'safety cock' position.
In this view the hammer is fully cocked and you can barely see the Rear Sear holding the hammer back in the full cock notch.
The way the action works is when you pull the trigger to fire the gun in double action mode, the Front Sear (the claw) rises to push the hammer back. At the final movement of the trigger a bit more resistance will be felt. At this point, the Front Sear pops forward, allowing the hammer to fall. When the hammer is thumb cocked for single action fire, the Front Sear goes along for the ride, and the Rear Sear pops up to hold the hammer at full cock. When the trigger is pulled, the Front Sear pops forward enough to allow the hammer to clear it, and at the same time the Rear Sear is withdrawn from the full cock notch to allow the hammer to fall.
I am trying to understand your description of what is going wrong. As I said, when the trigger is pulled double action, the Front Sear should pop forward at the end of the trigger stroke, allowing the hammer to fall. The hammer should not lockup when the trigger is pulled double action. And for single action operation, again the Front Sear has to pop forward at the same time the Rear Sear disengages from the hammer, so the hammer can fall forward.
Regarding taking one of these apart, first make sure you have some decent hollow ground screwdrivers. Do not attempt to take one apart with cheap hardware store screwdrivers. The wedge shaped blade of a cheap screwdriver will attempt to rise up out of the slot. If it rises up while you are applying torque, you will bugger up the screw slot.
Remove the large screw at the center of the side plate. This is actually a slotted nut, not a screw, but it does not matter. DO NOT attempt to pry off the side plate. You will scratch it up. The proper way to remove the tight fitting side plate on a S&W revolver is to grasp the gun loosely in your left hand, and strike the grip frame with something that will not damage it. The hickory handle of a hammer is good for this. DO NOT use the metal end, use the wooden end. Strike the grip frame just below where the frame is full width. As you strike the grip frame, the side plate should begin to rise up. Keep your thumb on the side plate so that when it pops free it does not fall onto the floor.
I have removed the side plate from dozens of Smiths this way, and I will tell you that this little guy was one of the toughest ones I have ever removed. I had to whack the frame quite a few times before the side plate started to rise.
I am going to suggest you do not go any further trying to remove any of the parts. It is tricky. You can clean and lube everything just the way it is. Get a pile of Q-tips and some rubbing alcohol. Using Q-tips soaked in alcohol, thoroughly douse every thing and rub off any old coagulated grease. Follow up with a few good blasts from a can of canned air. Be sure you have completely dried everything out. Then lightly coat everything with a light oil, such as Rem Oil. If cleaning and relubing the gun like this does not clear up the operational problems, reinstall the side plate and bring it to a gunsmith who has experience with this type of revolver.
Good luck finding one.
P.S. If I was going to fire this little guy, I would only shoot it with ammunition loaded with Black Powder. In that case, I would lube the inside with Ballistol, not Rem Oil.
P.P.S. To remove the cylinder, open the frame and lift the latch up with your thumb. Turn the cylinder counterclockwise while pulling up on it slightly. There is an interrupted thread at the rear of the cylinder arbor. Rotating the cylinder counterclockwise will engage the thread and allow the cylinder to rise off the arbor. Reverse the process to reinstall the cylinder.