This is an old thread, but I'm still surprised.
Witches actually don't need wands once they buy the "magic hands" lifetime reward. So the interface is designed so that magic can be used just with the wand in inventory. You don't click on the wand to start using magic. All you can really do from the wand itself is move it around and make it the sim's "preferred" wand.
To play with magic or to have the sim cast a charm on herself, click on the witch directly. To cast a spell on another person, click that person. To cast a spell on an object or the ground, click the object or the ground.
Keep in mind, the only two things a newbie witch can do is play with magic and conjure apples, (click on yourself). Other spells need to be unlocked by leveling up the hidden magic skill. Which is leveled up by using the magic you do have.
Does that help?
If not, it is entirely possible if you traveled recently, cheated to re-enter create-a-sim to convert the sim to a witch after she was created, or even if something went randomly wrong with the process of saving the game that a witch sim can end up bugged. If that's the case, than the only thing I can suggest is to try reloading from an older save. Otherwise you may need to use a potent cure to clear the bugged supernatural state followed by a witches brew to make the sim a proper witch again. (Which also means you need to brew them with Alchemy skill or find and buy them at the Elixir store.)