[RPG] How to deal with a player who is a bad sport

I have a dedicated gaming group that meets every Sunday. We have been playing regularly for over a year now. It's small, just 5 of us including the current DM. We all rotate DM position per campaign so that we can all have a chance to be players.

One of our players is a very poor sport, both as a DM and a player.

As a DM, their game was full of heavy railroading and resentment towards the PCs. At some points, they would even usurp control over the PCs and demand we feel or react a certain way, even if it did not fit our character.

Things such as "You can't attack the enemy. That's your sister. You wouldn't attack her. You feel too depressed to even swing your sword,".

They would get unreasonably upset and argumentative if we questioned these rulings, so we simply accepted them. When the campaign finally ended, they had a very emotional reaction at the table because the ending did not turn out as they expected. Our characters died instead of saving the world. They told us this was our fault entirely because we had made selfish decisions and not done the exact right things to complete the quest.

No amount of consoling seemed to satisfy them. All of us tried to tell them we didn't play games to win, just to have a good time and spend time with one another as friends. This didn't seem to help that much, and they then refused to ever bring up the subject again and would willfully ignore any attempts to resolve it.

As a player, they struggle with playing nice with other PCs and being open to character development.

They have a particular bone to pick with Charm Person-type spells or successful Persuasion rolls. Any indication their character's opinion may be swayed or changed, by magic or by a dice roll, is met with a huge amount of arguing. They will flat out deny the roll worked, will refuse to accept the DM's ruling and insist "No, my character DOESN'T feel that way. You can't force them too,".

This gets awkward when it's stuff done in good fun; for example, An evil spellcaster using Charm on their PC to force them to find them amiable and stop attacking. They will agree to stop attacking but will refuse any "roleplaying fluff" associated with the roll and brood over being forced to act against their character's nature.

They will do this with other PCs as well. They often play a Chaotic Neutral character who refuses to work with the party unless compelled by magic or high Persuasion rolls, but then will become icy and resentful out of character that they were "forced" to do so.

I have also noticed that they fudge their dice rolls.

They will purposefully use difficult to read dice, or they will snatch their dice up before anyone can check their roll.

We can't talk to this player. So I don't know what to do.

Not playing with them isn't an option. They are the best friend of another player, so if we stopped inviting them or asked them to leave, it would likely just dissolve the entire group. (This best friend acknowledges the problem player is a problem, but they don't want to game without them.) These are minor gripes that I hope to find an amicable solution to rather than that.

We have all tried individually talking to them about their behavior, which they will ignore or just shrug off. They won't even directly answer a question, or they will claim they didn't notice.

How do you deal with poor sports at the table?