As soon as you involve mods, things get tricky. Without knowing which mods are involved, its hard to say where the bug comes from, and even then your only recourse might be to enable and disable mods systematically to find whichever one is causing it.
Isolated the error now. If I enable Skyrim Redone (Sky Re), I suddenly cannot pick locks anymore.
Until further notice 21st of October, please DM me for important stuff, and let the game master control my characters