I used my user id in the name instead of the user id text field, when I made the comment.
Jeremy, the rules of f.i.d.e. chess states that you can't capture the enemy king.
In the case of the idea that I was talking about, where 'mating' the king on the first turn not result in a win (because not moving on the next turn would not count as not having legal moves), 'mating' the enemy using the first of your two turns, would not result in a stalemate situation, if the player is still able to make a movement on the second turn that not capture the enemy king.
Jeremy said: 'The obvious generalization of the rules of check is that the king is in check if it could be captured before the owner's next move'
So this generalization means that the 'the opponent has no legal move.' part of this rules: 'The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move.', means that: Not being able to move because the next turn is the enemy one, counts as having no legal moves.
With that this means that the variant I was creating would be:
Turn order: White, Black, Black, White
If you mate the enemy king on the first of your two consecutive turns, he would not have legal moves (because the next turn is your turn), so you win the game.
Also using this generalization of the rules you wouldn't need to check if king could be captured within 2 moves, only the first one.
The player would be able to put his king in a situation where the enemy player can't put him in check using the first of his 2 consecutive turns, but would be able to do that in the second one.
In f.i.d.e while choosing what movement you will do, you only for check the within next enemy turn.
The key thing here is something I maybe forgot to say/explain about my variant idea: The 2 consecutive turns, are not '2 turns into one', but different ones. The thing is that the turns are alternating, first the turn order is white, black and then the turn order changes to Black, white, then it changes again back to white, Black, and then it changes again...
Thanks George Duke, I usually search here, but most of the time only to check if there is already chess variants with some variant name I was thinking about, also the variant is not finished yet.
Also the ideas I get with this variant will be used on other variants I am creating, even if there is a variant that is 100% equal my one, the ideas of this variant will still be usefull.