I have said here quite a few times that in
my opinion, "positive thinking alone" is not enough. If we could simply think happy, positive thoughts all the time, and that was enough to solve all our problems, we'd have done it already. We wouldn't need so many other skills & tools.
Tony (Anthony) Robbins, who most people think of as the most famous "positive thinking" coach, says the same thing. Actually, he's where I got the belief from.

(I will be staffing Tony's NJ/NY Unleash the Power Within event next weekend.

This is my 12th year staffing his live events, around the country, on & off.

So you guys/gals are probably going to read a lot of examples & processes in the next several days from me, as I'm back in the Tony mindset for a while.
Tony says all the time that, "You can't simply go around thinking, 'There's no weeds, there's no weeds.' The weeds will come & take over your whole garden. You need tools, skills and techniques to change things."
Thought patterns and emotional patterns become habits that people fall into without realizing it. There are about 19 different emotions, but in an average day, most people only experience about 5 of them. That also becomes their comfort zone. Some emotions even become addicting.
You know someone who is angry all the time. No matter what you say, what the situation is, they immediately find some reason to become angry.

Someone else is a drama queen or loves to create chaos all around them. It's a nightmare for everyone else who doesn't want to be in such volatile situations all the time,

but these people actually feel "alive" when they are in the midst of a crisis.
That's their addiction. They generally don't know how to be in
other emotional states where they can feel
equally alive, so they keep going back to creating & having dramas. They don't realize they can feel equally alive by winning and accomplishing something meaningful.

Or they lack the resources & techniques to do it. (Which is why positive thinking alone is not enough.) But they are
pros at destroying and creating havoc.
Sounds, like your kids have fallen into a "negative" pattern. You didn't mention how old your kids are. Nowadays, for kids, being snarky & negative is a cool thing to be.

To not care about stuff.
Some of the time it is used as a defensive mechanism at school. If another kid knows they care about something & they can break it or ridicule them for it, they have power. So kids learn to shrug & pretend not to care, or to speak negatively about stuff, so they aren't seen as vulnerable. They may also learned to attack first, so they have the upper hand and take power from another. (That is a control drama, discussed as Insight 4 in
The Celestine Prophecy.)
The problem is when it becomes a
habit to think that way. Thinking positively may be a muscle not used very much by your kids -
at the moment.
Thinking "negatively" is not all bad, there are good traits. The good side of arguing is, if your children enjoy arguing, I see potential Debate Club winners in high school, if their arguing/debate skills are honed right. Some members on the DIS would love to have the Debate Forum reopened. The Mods say the problem is, they don't really debate, they annihilate each other.
If your kids are the right age, start teaching them the difference of arguing a topic, as opposed to putting down each other. It's good to raise children to analyse, speak up, have their own formed opinions and not just docilely follow the crowd like sheep.
"Negativity" used as critique and problem-solving is a good resource to have. Walt Disney in creating the Imaginarium think tank, had a room for his team to create all the ideas & dreams possible, and a
separate room for critical analysis & problem solving of those ideas. Challenge the kids to problem solve instead of argue. It will be one of the most valuable tools you can teach them. We live in a society of "learned helplessness" where people who are
fully capable of doing things, fall into a helpless, victim mindset, and complain or blame, instead of figuring things out.
To get them to think more positively, you
first have to
interrupt the pattern as they go right into that negative thought pattern or are already in one. Catch them and stop them.
I can't stress Pattern Interrupts enough. It's harder to change things when the train is already barrelling down the tracks full speed.
Pattern interrupts happen all the time. We just don't realize it. When a toddler falls but doesn't get hurt, there is a split second where he doesn't know whether to cry or just be surprised. If you grab his attention in that moment and divert it, you stop him from automatically going into unnecessary crying mode. Same with taking a toy or item from a child and diverting his attention before it turns into a screaming fit.
If one of your kids yelled from the other room right now, "Hey, what's all those bubbles coming out of the washing machine?!?" That would be a pattern interrupt

as you stop what you are currently doing to focus on that. Same for if you heard the dog got out of the yard. Or if your boss walks in and says, "Where's that blue form for the project?"
Sometimes you see a nosy relative making a bee line toward you at holiday dinner, and you know she's going to start asking personal, inappropriate questions. You
interrupt her before she even starts in, by complimenting her on her hat, asking her about everyone else, then make an excuse to talk to a cousin before she asks about you.
You know when your kids or spouse interrupt their own pattern, when they are suddenly all smiles,

complimenting you, doing things for you, and you become all suspicious, because they don't normally behave that way. What do they want? What have they done that they are diverting you from, trying to butter you up & put you in a good mood for?
Pleasant pattern interrupts are if the same boss walks in and gives you a $5 raise because that blue form saved the day!

Someone gives you a compliment, when you were having a bad day. Someone gives you a gift. Publisher's Clearing House is standing at your door with a check.
Catastrophic pattern interrupts are debilitating illness, divorce, being fired.
Use a positive pattern interrupt to stop the negative pattern.
Then Challenge them to think differently. Make it a game. Make it fun for them to out think each other in fun positive ways. Part of arguing is the feeling of winning & topping each other. Make it a game to catch themselves or each other (without shaming,) when they have a negative thought, and to turn it around by coming up with 3 positive thoughts, or 3 things that would solve their problem. They will barely come up with one at first, but the point is to teach them there is more out there than what they are currently thinking.
When I'm in the Tony Robbins staff room at an event, I have long since learned, not to say anything negative, whiny or complaining, unless I'm prepared to have someone in listening distance, in a supportive way, interrupt my pattern & challenge my thinking. In the early days, (and even now,) sometimes it
feels better to have a whiny, victimy, hissy fit. But it doesn't accomplish anything. Wrong crowd. Sometimes, they will even let me have my hissy fit,

THEN I have to come up with 3-5 ideas to solve the problem.

If I can't come up with any, they and 3 other people, who have now come in on the
fun challenge, will
easily rattle off ideas,

or start brainstorming & working off each others ideas.

Whereas, I was more committed to expending energy on a hissy fit.

For us, it's about making each other
aware when we have a less than empowering moment and we have choices of how to proceed. We supportively hold each other accountable to a higher standard.
It also makes us see, okay, we had a hissy fit, when we could
just as easily have come up with 3-5 ideas. It's about deciding which muscle we want to flex.
Expect resistance at first. But persist. Remember, this is an under used muscle. Their brains are not going to want to get off the couch to do this. They'd rather go back to their well used, comfortable patterns. As you challenge your kids, it will help you too, to flex that positive, problem solving muscle. You have to lead them and then to stay up with them.
Have a prize or reward that they will want at the end of a day, for the one with the most positive ideas.

Make it a
valuable game for them to play. It doesn't have to be money. Maybe they get to pick dessert, or to have their favorite meal on Friday nite. Soon it will become a way of life, to think that way.