The Stevens doubles are pretty simple and if it opens fine before fired, then it should open fine after firing (in theory).
If the pins are not sticking in the primers, then you can rule that out.
Another thing to check would be if it is in fact the cocking mechanism. The Stevens 5100 (311) cocks by the barrels lifting an arm in the base of the action. What I would do is uncock it (by dry firing it against a block of wood as to not chance breaking the pins), and then assemble the gun and open it (to cock it) without anything in the chambers. If it opens fine at that time, then the issue is related to the shells being in the chambers.
What type of ammo are you using? I have found that some of the cheap Winchester target loads (from walmart) what to expand the matal base when fired and make them stick up in the chambers of some guns. This also loosens the metal base on the shell as well. I have had some guns where I cannot put a fired shell back into the chamber due to the expansion of the shell base.
I also once had an ejector single shot that would not eject the shell due to this issue as well. Talk about a pain in the ass at the trap range...
