Hi everyone,
So imagine : a player character betrays the group and attacks one or any of them in a skirmish (or a duel for that matter).
What about the action order ?
-2 or more PCs only in the field but 2 sides -
Does the GM still decide which act first ?
Who can use the momentum ?
If only one side can use momentum how threat is spent by the other “player’s side” (by GM’s choice or player’s choice) ?
How avoid metagame abuse (like depleting the threat /momentum pools intentionnaly) ?
If you are getting into a situation where the GM is having to dictate how the players can spend the group momentum pool against each other then you have a major player problem.
Inter group conflict can be great RP, but the players have to be on the same page and not trying to use player mechanics to gain an advantage for their character.
As a GM my resolution of the specific questions would be:
The only way I would change the base rules for the players is if one of them became a DPC. (Directed Player Character) In this situation they are essentially relinquishing some of their control to the GM.
This is basically where the player and GM are scheming together to develop the plot by means of the betrayal.
At that point the conflict is still directed by the GM and so normal rules for NPCs apply and the character doesn’t use Momentum so the whole pool stays with the main party.
Not the time being. That’s pure projection of the worst situation between players. But just in case. 
The “betrayer” having to give Threat to the pool instead of spending Momentum could convey the sense of doom of an unexpected betrayal of a trusted friend.
Yup, very much depends on the circumstance.
Certainly there would still be two sides.
Initiative isn’t ‘players then NPCs’ its ‘side A vs side B’ so thats still works as normal.
Momentum is stickier, but depends on the GM.
While skirmishes are players being a pain to each other, I can easily see an honour duel going on between PCs.
I’d say if the players are being a pain then they can share the momentum.
Which does mean good rolls from either side are giving the other side points to use.
Might change a few tactics.
While this might seem odd it represents the players all knowing each other’s tactics and weaknesses.
Failing that, if one PC is under someone else’s influence or being manipulated by the bad guys they could be the one to use the GMs threat.
Otherwise, you could ban both from using momentum.
This only works if there are a lot of contested rolls where they are setting each other’s difficulties though as the system assumes a free spend of momentum to hit the higher difficulties.
So think carefully about that one before taking this route to ensure they still have a decent chance of succeeding.
Another route might be to have two momentum pools for each character. That’s the only way I can see a Player-vs-Player duel working as intended. Ignore Threat for the duration, anything that would generate Threat is instead added to the opposing player’s Momentum.
This is something I’ve actually given a lot of thought to, after I had the idea of running Dune with multiple groups and each was a different House feuding against the other. The 2d20 system has the unique stumbling block of how Threat/Momentum works in PvP and while usually you can just say “Don’t do it” that’s not an option in the scenario there. I feel that Dune is a setting that might be uniquely suited to such play, but a PvP fix is needed and having multiple Momentum Pools is the only workable one I’ve come up with.
I would suggest that the Momentum Pool of one group is the Threat Pool of the other: Every threat one group adds to the Threat Pool becomes Momentum for the other group and vice versa.