So, a bit of a backstory on this. Player A has been difficult to play with as of late, making characters that despite being good begin stealing or killing or withholding important information from the party out of nowhere and being a general nuisance regarding the role-playing aspect.

We're in a homebrew campaign set 20 years after the "Fall", an event that wiped out most of creatures and turned them into something else... The campaign is called "Death Valley" and our DM warned us beforehand that it would be ruthless and we needed to be prepared to lose our characters at any second. We were all fine with that and opted for a challenge. He also stated that we could all choose any number of common-uncommon magic items at the cost of being a bigger target; the more loot you have, the easier it is for enemies to spot you cause you're basically a beacon of arcane energy and valuables.

So we all rolled our characters at level 3, mine being a Goliath Zealot Barbarian, player B's being a home brew Ring Wraith class, Player C's being a home brew Lore of Metal Bard and player A had a Gnome whose class he never mentioned cause he wanted to keep it a secret. We all guessed him to be a wizard or a sorcerer though and we were correct when he began casting spells and doing absolutely everything in his power to avoid being hit in combat to the point of not even assisting us.

Now, most of our PC's didn't have anything too crazy regarding their magic items. Everyone had at least 1 to max 3.... except the Gnome who turned up with 8 making our party the biggest target in all of this mad max esque world. He was worth more than anyone of us had ever seen but we played nonetheless after explaining to him that of he dies or we get into a rough spot as a result of hunters and scavengers tracking us, it's on him.

The first mission was to extract water from underground, beneath a land long forgotten, riddled with the bodies of warriors that fought in wars before the Fall. We had a week to get there, extract the water using special metal rods, fill the 15x15 barrel to the brim and come back, in exchange for loot. Now, I must note that If we failed or lost anything regarding the mission the punishment would be severe. So we hopped on our cart attached it to the barrel and off we went, opting to take the mountain trail instead of a swamp/forest area when we came to a split due to it being faster and easier to observe our surroundings in.

At some point on the trail we spot a megapede feeding off of a pile of soldiers about 600ft ahead of us at which point it shifts it attention to us and begins slithering toward us. We then realise it's a mount for a half elf Hunter and I suggest we begin to take up defensive positions. Player A said "Well you can go fight it, I'm staying here."

Me, not wanting to start an argument OOC, reply IC that he can stay and watch the cart and barrel and to assist whenever he sees we're in a rough spot.

I got no reply, but me and the rest of the party got off regardless and advanced towards the slithering creature only to spot an additional one descending the mountain and attempting to flank us. It's rider shot at me with his bow and combat began, during which, the gnome was playing card games with the mules dragging our cart and levitating mid air doing absolutely nothing of what my character asked him to.

Player B goes unconscious, Player C has been thrown off the steep incline and is rolling Athletics checks to climb back up and I'm up there with 5hp fighting an injured megapede and his rider after having shoved the other two down the cliff. I stabilize Player B's Ring Wraith and I ask Player A both OOC and IC for assistance to which he replies "Yeah, when you look at me you notice I'm levitating."

"Okay...? Can you... distract it? Throw one of the rods near the megapede."

He asks our DM, "Can I throw it?"

"Yeah sure why wouldn't you be able to throw it?"

"Okay, I cast firebolt on the megapede"

And proceeds to cast it for like 3 damage.

I go down after I decapitate the half elf and begin rolling death saves while the gnome flees the scene and leaves our rods to be devoured by the megapede's consume metal feature.

I roll a crit, come back with 1 hp and use up all my speed to stand up and dash to it. It pays no mind to me and begins eating the spare rod as I rage and attack recklessly.

Another Nat 20 and I rolled somewhere around 30 damage, killing the–thankfully already injured–megapede and making a futile attempt at gutting it in hopes to save any of the rods.

We go back to get another set of rods but, you know, we had to be punished. The royal that gave us the mission was feeling generous that day he said and instead of punishing the entire party he'd settle for two of the members to carry the weight of the responsibility.

Player A of course states that he's not taking any responsibility for it and that the blame befalls the entire party. Again, in order to avoid an OOC confrontation I jokingly suggest to player B that we could be the men of the situation and take the responsibility.

I won't go into much detail but I ended up losing an arm and 11 points from my hp max and player B's character lost an eye and 9 points from his hp max.

After that we went to trade some loot for weapons and armor cause I couldn't really use my Greataxe anymore and player B's Ring Wraith needed a new armor as his old one got eaten by the megapedes.

Off we were again, taking the same trail as before and making it quite some distance away from the first encounter before being ambushed by some earth elementals. We fight, Player A' gnome falls unconscious and none of us could really get to him, though, even if we could, we were all really low on health and I had ran out of rage fuel.

Gnome ends up being taken away into a cave up in the mountain range located in a spot we couldn't really climb to and he is asked to roll another character.

We all gain a level and are met with a Frost giant ascending the cliff next to us. We try to fight but end up running away down the decline. The Bard has a broom of flying but is struck by a boulder mid air so he goes down, the Ring Wraith holds onto a tree and rolls well enough to jump over another boulder, saving himself and I'm stuck rolling down the cliff, making a makeshift ramp using my axe to dodge the boulder and being slapped into the air by the giant soon after only to be snatched by a griffon and eaten cause I was left with 2hp.

Turns out the griffon was player A's new character's pet, who saved the ring wraith and carried him back to his home. I rolled up a Tabaxi Open Hand Monk and Player C made a Half-Orc Death Cleric.

Cut to our latest encounter, the creature we were fighting against dished out damage within 5ft every time it took a hit. Player C's Cleric goes down next to it and takes a hit from the creature causing him to sport two fails on his death saves before he even has the chance to roll. Player A's turn is up. He knows full well that the creature causes damage within five feet of it and instead of stabilizing the Cleric or at least doing something other than what he ended up doing, he says OOC "Well, you did let my gnome die" and attacked the creature, killing it along with the Cleric, who lasted for about three hours after being introduced.

I honestly don't know what to do at this point and I've talked with everyone in my group. I've sat him down and talked with him more times than I can remember and all I get as a reply is along the lines of "Well this is who I am, deal with it."

I don't want him to stop playing with us cause he's generally pretty cool but he's just so difficult sometimes. I don't want to be the one always talking to him nor do I want to be the dude who's constantly in his face.

TLDR: Problem player caused the death of another's PC as revenge for his previous fallen one.