How to "manage" turn order?

I don't quite understand the exact processs you're talking about but I faced what might be a similar problem with my 'Nak Muay' card game, so I'll describe the solution I came up with which I'm pretty happy about.

The theme and feel of the game demanded that the guy with initiative play his cards first and the other chap response.

But playing second had a natural advantage: you know what you're countering. The second player has the advantage of information. This was bad.

I toyed with solutions like heaping various bonuses onto the initiative guy...but it felt artificial and contrived.

My system now is, the initiative-chap places his attack first, with a hidden bid.
The opponent (if he chooses to attempt a counter) places his own attack and (hidden) bid.
THEN the attacker has the privilege of declaring the winning condition of the bid:
Will the winning bid be the one with the highest total (bids have 2 numerical cards)?
Or the one with the highest card - regardless of the sum total?
Or...will the attacker declare "best pair", in which case the highest pair will win (and only pairs will win)

So, I suppose one way of dealing with your issue is to let the first card-layer also be the one who decides something important. Otherwise, as you described, going second is a natural advantage because you have more information.

I'm sure you have your own solution to this issue. This was mine. I'll be interested to read yours. ;)

i dunno, usually with my games and commercial tcgs its just turn by turn, player 1 has its turn then player 2.

Next game im working on, i want the defending player who is not having their turn to block attacks, that is what im doing with the dice mechanic,i want the defending player to be engaged in combat when not their turn. it might work for other games it depends how you implement it

Player one at its end of its round, plays new cards. These new cards start exhausted.

Player two will not be bothered by the new cards, since they are still exhausted. So any thing from player two could attack, maybe even attack the exhausted cards if their defence is low enough.

Player one can now take the exhausted cards into full play.

This is a bit different than MtG. Where new cards are not exhausted when they come into play. But then the reason is that they can defend. I say, exhausted cards are sitting ducks. So, now you get a strategy of bringing weak defence/strong offence cards into play, only if there is some fodder to use.

That is a nice approach, let-off studios. I didn't even think about 3 or more players.
It sure intensifies choices. So I put this mechanic in my ender chest. :)

Definitely agree with this. Very cool to have different pros and cons related to taking initiative vs countering.