Joan Covenant is the ex-wife of Thomas Covenant and the mother of Roger Covenant. She appears to a greater or lesser extent in all three Chronicles. Looking at both her and his choice of second wife, it can only be presumed that Covenant has appalling taste in women.
Role in The First Chronicles
We actually don't see Joan at all in the First Chronicles, since her primary role in events has already taken place before the story has even started. Here's the scoop.
Having married Thomas Covenant in a ceremony involving the swapping of white gold wedding rings, and having borne him a son, Roger, life is looking just peachy for Joan. Her hubby has become an acclaimed novelist and the family has moved into a farm in the country where she can indulge her passion for all things horsey. However, a big oops is just around the corner - Covenant is discovered to have developed leprosy all of a sudden. That's going to put a kink in any relationship, one would think.
Joan is utterly aghast when she finds this out and is completely unable to handle the situation - perhaps she is worried that she'll find the occasional toe in her hubby's socks that she's about to launder, or maybe she's concerned that when making the marital bed in the morning, she may discover... no, let's not go there.
Anyway, Joan takes Roger, her infant son and hightails it out of town, filing for divorce in the process. This clearly does nothing to improve her husband's mood, but then again, you can't really have a happy and sunny anti-hero, can you?
Joan makes a very brief off-stage appearance in The Illearth War, when Covenant receives a phone call from her, which is cut short by his being suddenly whisked off to the Land for the second time, a thing which adds yet more to his already extreme grumpiness.
Role in The Second Chronicles
During the start of The Wounded Land, we find that Joan has returned to the Covenant farm, but unfortunately for TC, she's well on the way to being a permanent resident of Froot Loop city. Covenant is doing his best to look after Joan, even though she does her level best to beat the living crap out of him whenever she's got half a chance. Yes, sadly Joan is mostly crazier than a sackful of weasels, no doubt partly through guilt at having dumped him in the first place, but also because she's fallen under the influence of some Moonie loony cultists, who despite being in the "real world" worship Lord Foul. These are the same weirdoes that Jeremiah's birth mother is a member of and are the bunch of sickos responsible for the maiming of his hand (and indeed, all of their hands) in the eldritch fire via which they are trying to conjure up the Despiser.
Incidentally, Covenant and Linden meet for the first time when the former pays a visit to the Covenant farmstead to check on how TC is is getting along. Thoolahian scholars insist that the mere presence of Linden in the same house is liable to have pushed Joan entirely over the edge into inescapable madness.
Anyhow, the Lord Foul loonies kidnap Joan and are about to sacrifice her when Covenant, in a fit of staggeringly bad judgement, offers to trade his life for hers. This bargain is gleefully accepted and at the very point that a knife is driven into his chest, with a special effects whoosh, Covenant (with Linden in whiny tow) is transported off to the Land again, leaving mad-as-a-fish Joan behind.
Role in The Third Chronicles
At the start of The Runes Of The Earth, we find that Joan's incarcerated in the local nuthouse, where, in a sickening twist of cruelty to make matters even worse, Linden is the doctor in charge.
Joan is by now completely, utterly, totally, foaming at the mouth insane and has to be restrained to prevent her from beating herself up - although in Houdini-esque fashion, she always seems to find an unseen way of slipping her bonds. The only thing that seems to calm her at all is the presence of her white gold wedding ring that she wears on a chain around her neck.
Enter the next baddie from stage left to a chorus of boos - Roger Covenant. Now an adult in his early twenties, Roger does not come across as a particularly nice individual. It's immediately obvious a) that he doesn't give a rat's ass about his mother and b) that he's up to something. This is swiftly proven when Roger kidnaps his droolingly nutso mom at gunpoint - shortly after abducting Jeremiah, Linden's slack-witted adopted son as well - and heads off with his captives to the old Covenant farmstead. Linden rushes after them in hot pursuit, only for all four protagonists to be struck by magical lightning while caught in the middle of a gun battle with local law enforcement. It's unclear whether any of the four have been shot, but that scarcely seems to matter, because Shazam! it's off to the Land again.
It transpires that Joan has been possessed by Lord Foul for many years and when she arrives in the Land, she materializes on the cliffs near Foul's Crèche. There, tormented by a Raver and kept nourished by skest, Joan's madness, augmented by the argent puissance of her white gold wedding ring, takes shape in the generation of Caesures, cyclone-like manifestations of insanity that rip the fabric of time and space apart. These she causes by slapping herself upside the head. Joan is slowly destroying the Land bit by bit - and ironically, it's only the fact that her madness has left her with the attention span of a caffeine-crazed goldfish with ADHD that means she hasn't yet caused more destruction.
Having been recombobulated from beyond the grave at the end of Fatal Revenant, Covenant decides in Against All Things Ending that he really needs to do something about his ex. So off he heads to Foul's Crèche, along with two Haruchai and a couple of Ranyhyn. When after great travail he finally meets up with Joan, she's not best pleased to see him, to say the least. At which point Covenant makes his divorce ultimately final in rather sneaky manner - gesticulating ecxitedly with one hand, he yells to Joan "Oooh honey! Just look at those pretty horsies!" While she is thus distracted, he stabs her with Loric's krill, putting her out of her misery once and for all and swiping her wedding ring while he's about it.
As a side note, this finally frees up TC to marry Linden - though frankly it's hard to decide out of Joan and Linden who makes the less desirable spouse. Rock and a hard place, if you ask me.
Appearance and Personality
Since we don't actually see Joan on stage until after she's gone batshit mad, it's hard to ascertain much about either her looks or personality. One can suppose that originally she must have been a reasonably attractive woman of a similar age to TC himself, but presumably guilt-inspired insanity really isn't much of an effective beauty régime. As we see her in both the Second and the Third Chronicles, Joan is the archetypal howling nutcase, painfully thin with wild hair like tangled brambles. By now she has a mad light permanently flickering in her eyes, has lost most of her teeth and is covered in self-inflicted bruises. Not to put too fine a point on it, but she's not going to make the Miss World qualifiers.