Yes there is a way to take it back apart. What has happened is your hammer is not all the way forward when you are trying to disassemble the pistol. The hammer strut is causing the mainspring housing to get stuck when trying to remove the assembly. Insert an empty magazine into your pistol and squeeze the trigger. While holding the pistol muzzle down, keep the trigger squeezed fully to the rear and try removing the mainspring housing. NOTE- You cannot remove the mainspring housing in a 22/45 with a magazine inserted, the latch won't release and clear the frame.
If it still won't release then here's a next step. You want to get a block of wood (piece of 2X4 stud) and set it on the floor or a hard surface. You will next take the pistol, insert an empty magazine again, squeeze the trigger and hold it, then tap the pistol firmly on the barrel muzzle end onto the block of wood. This should cause the hammer to move fully forward and release the mainspring housing. Try removing the mainspring housing again.
Lastly, there's a manual way to release the sear in a Mark II/III pistol. You'll need a scribe or another small metal tool to manually release the sear. A long flat bladed screwdriver to press the Mark III magazine disconnect safety lever, to release the sear. First remove the grips on your Mark III pistol. Insert the long flat blade screwdriver and depress the magazine safety lever to release the sear. Next reach in and hook the sear with the scribe and pull downwards to release the sear. Here's a picture of the process.
Once the sear has been manually released, the mainspring housing can be fully removed and the pistol reassembled again. Be sure that the hammer is in the FULL forward position prior to inserting and closing the mainspring housing. One way is to use a metal tool to push the hammer forwards like in step #6 of this fieldstrip procedure:
http://www.guntalk-online.com/fsprocedures.htm
Hope this helps. One of these steps will work for you.
R,
Bullseye