In putting the side plate back on, which ever side you pick first you have to push that trigger forward so that the sear goes on top of the trigger plate. If not the sear will be pushing against the trigger plate and you will not get the side plate to go on.
If you have both side plates off, you can look into the hole where the sears go through and see the trigger plate, move the trigger forward and you will see the trigger plate move downward.