The not firing until the second hammer drop may not be due to the mainspring.
A weak mainspring will often allow the hammer to blow back to half cock when the gun is fired.
If your hammer did not do this then you should look at other things that could cause it.
In order to fire reliably the priming compound must be sitting right against the end of the nipple.
If the nipple is too large for the caps your using the tapered body of the nipple will hold the priming compound above the end of the nipple.
Then, when the hammer falls it seats the cap as it should be. The next hammer blow fires the gun so it seems like the mainspring is too weak when in fact the nipple was at fault.
Many times, especially with older guns which have had previous owners dry fire them, the end of the nipple will be mushroomed.
This can easily keep a proper fitting cap from seating like it should.
Look at the top of the nipple. If it looks like it is mushroomed at all, or if it looks like it is slightly swollen from repeted dry firing all you need to fix it is a new nipple or a small flat file.
With poor fitting caps/nipples I usually chuck the nipple in a electric drill locating the chuck jaws on the body of the nipple (not the threads).
Then, with the drill on my left, pointed towards my right side I start the drill slowly and rest a flat file against the cone of the nipple using the nipples cone angle to align the file.
With the drill running, a few slow forward strokes of the file will remove a few thousandths of an inch worth of material.
I then try the cap. If it fully seats, I'm done.
If it still seems to be hanging up I repeat the filing.
Give it a try before trying to find a new mainspring.