A picture which is Fluff should never be used to regulate rules of the game. No where in the description of the Klar does it mention that you can hold items, use an off-hand weapon, or use a two-handed weapon. If it doesn't say it in the description then that simply means you can't. To put it another way ask the player to show you in the Klar description where it says she can use it with a two-handed weapon or be able to keep the +1 shield bonus while using it as an off-hand weapon.
Your players seems to be mixing the rules of a buckler with a the rules of a klar. If you feel generous you could maybe allow a Klar to keep its +1 shield bonus while being used as an off-hand weapon if the character takes the Improved Shield Bash Feat, but truthfully its not a shield bash so by core rules it should not work.
Not to be mean in this question, but who is running the rules for your game the DM or the players? ;)
Hope this helps.
There's a feat in PF #10 A History of Ashes that allows someone to use an earthbreaker and klar as if fighting with a double weapon.
Thunder and Fang
You have mastered the ancient Shoanti fighting style of Thunder and Fang, allowing you to fight with increased effectiveness when wielding an earthbreaker and a klar. As you swing at your foes with Thunder (your earthbreaker), you slash at them with the Fang (your klar).
Prerequisites: Str 15, Two-Weapon Fighting, Weapon Focus (Earthbreaker), Weapon Focus (Klar)
Benefit: As long as you are fighting with an earthbreaker and a klar (and make attacks with your klar as your offhand attack), you can fight with both your weapons as if wielding a double weapon and retain your shield bonus to your Armor Class granted by your klar. Treat your klar as a light weapon for the purposes of determining your total penalty to attack.
Special: A fighter may select Thunder and Fang as one of his bonus fighter feats.
The inferences are that 1) a klar is treated as a buckler, allowing the use of weapons with a -1 penalty to attack rolls and 2) attacking with the klar or a weapon using the hand that the klar is on prevents you from gaining the AC benefit, just like bashing with a shield (without taking a feat to allow it; I'd recommend having Improved Shield Bash apply to a klar).
When I first saw the Klar, I said 'Oh. It's a spiked light shield that does a different damage type.' I been pretty much treating it that way.
That said, the Thunder and Fang feat does imply that the Klar is a spiked buckler, rather than spiked shield. Since bucklers can't normally be spiked, this does make it a more powerful item. But probably not game-breaking.
But you should look at the rules for light shields and bucklers to rule what hte player can and can't do with their Klar.
There's a feat in PF #10 A History of Ashes that allows someone to use an earthbreaker and klar as if fighting with a double weapon.
Thunder and Fang
You have mastered the ancient Shoanti fighting style of Thunder and Fang, allowing you to fight with increased effectiveness when wielding an earthbreaker and a klar. As you swing at your foes with Thunder (your earthbreaker), you slash at them with the Fang (your klar).
Prerequisites: Str 15, Two-Weapon Fighting, Weapon Focus (Earthbreaker), Weapon Focus (Klar)
Benefit: As long as you are fighting with an earthbreaker and a klar (and make attacks with your klar as your offhand attack), you can fight with both your weapons as if wielding a double weapon and retain your shield bonus to your Armor Class granted by your klar. Treat your klar as a light weapon for the purposes of determining your total penalty to attack.
Special: A fighter may select Thunder and Fang as one of his bonus fighter feats.
I really wish I had known about this earlier.
There's a feat in PF #10 A History of Ashes that allows someone to use an earthbreaker and klar as if fighting with a double weapon.
Thunder and Fang
You have mastered the ancient Shoanti fighting style of Thunder and Fang, allowing you to fight with increased effectiveness when wielding an earthbreaker and a klar. As you swing at your foes with Thunder (your earthbreaker), you slash at them with the Fang (your klar).
Prerequisites: Str 15, Two-Weapon Fighting, Weapon Focus (Earthbreaker), Weapon Focus (Klar)
Benefit: As long as you are fighting with an earthbreaker and a klar (and make attacks with your klar as your offhand attack), you can fight with both your weapons as if wielding a double weapon and retain your shield bonus to your Armor Class granted by your klar. Treat your klar as a light weapon for the purposes of determining your total penalty to attack.
Special: A fighter may select Thunder and Fang as one of his bonus fighter feats.The inferences are that 1) a klar is treated as a buckler, allowing the use of weapons with a -1 penalty to attack rolls and 2) attacking with the klar or a weapon using the hand that the klar is on prevents you from gaining the AC benefit, just like bashing with a shield (without taking a feat to allow it; I'd recommend having Improved Shield Bash apply to a klar).
Should attacking with a klar be considered as an exotic light weapon or a one-handed weapon?
Buckler: 15gp, 1AC, - Dex, -1 ACP, 5% ASF, 5lbs, Cannot bash -1 to attack w/ wielded weapon.
Lt. Spiked shield: 13gp, 1AC, - Dex, -1 ACP, 5% ASF, 10lbs, 1d3/1d4 dam, x2 crit., light weapon, piercing.
Dwarven Buckler-axe: 20gp, 1AC, - Dex, -1 ACP, 5% ASF, 3lbs, 1d4/1d6 dam, x3 crit., light exotic weapon, slashing.
Gnomish Tortoise blade: 10gp, 1AC, - Dex, -1 ACP, 5% ASF, 4lbs, 1d4/1d6 dam, 19-20/x2 crit., light exotic weapon, piercing.
Klar: 12gp, 1AC, - Dex, -1 ACP, 5% ASF, 6lbs, 1d4/1d6 dam, x2 crit., light weapon, piercing.
Hvy. Spiked shield: 17gp, 2AC, - Dex, -2 ACP, 15% ASF, 15lbs, 1d4/1d6 dam, x2 crit., one-handed weapon, piercing.
The Dwarven buckler-axe and Gnomish tortoise blade are from Races of Stone and are not core, but the similarities between the tortoise blade and the klar make me believe they may be the same item. I added the buckler for comparison purposes but do not think the klar should be treated as a buckler. The fighting style of Thunder and Fang allow the weilder to treat the two weapons as a single item for attacking purposes, not as a two-handed weapon and a buckler. Nowhere in the description does it say buckler, nowhere does it say -1 to any attacks, and nowhere does it say you lose the benefit to your Armor class. All it infers is that the two items are joined together in such a way that you can attack as a double weapon and continue to gain the benefit of the shield bonus.