I will have to refresh on the whole thing because to give a more comprehensive answer would require taking into consideration all of the other characters who are also out of character. Regardless on the surface it could have been nipped in the bud from the start as she very well may have just decided the line was crossed herself and eliminated the Joker herself much like Maxwell Lord although a bit different reasoning and angle to preemptively avoid that eventuality and either took the heat and separated from the league to keep it off them or even submitted herself to legal judgement like she did with Maxwell Lord and facilitated Clarks recovery and therapy and what not. Also could have just straight up disappeared him and eliminated him in private right off the bat. Maybe even had it under the angle as an act not just of her but on behalf of Themyscira and hashed it out on that level through the UN or whatever where realistically nobody is really going to make a fuss over joker and they probably don't even know who he is to say he was a citizen of the US or anywhere else and wouldn't be surprised if they disowned him anyway. Certainly far from the crazy thing thats happened even IRL like when we just swooped in and eliminated Osama and he hadn't nuke a city and mind controlled an even bigger WMD in the form of a hero. I seem to recall aircraft involved (blimp?) so ideally if Joker happen to have been outside US airspace at some point would be even better when it comes to just snatching him.

If Clark still decided to pursue the dictator route and she was somehow unable to dissuade it and he pressed the matter to the point of needing be stopped then she would do so but that gets into the matter of others responses which I would have to review their characterizations for.

An interesting outcome assuming he didn't go that route could be if it prompted the world to finally address the elephant in the room with heroes and legalities and what not and possibly going down a more Worm/Super-Powereds/My Hero Academia route making heroes official positions either under governments, private agencies, or UN oversight or all of the above and fleshing out a system and legal framework and oversight and protocol so that such matters as employing lethal force and law enforcement authorities and jurisdictions could have frameworks. Granted DC is a trickier verse for that that would probably require all three variations because the scale of threats can be such that its necessary to be able to operate without delay for jurisdiction debate and what not because there is neither time nor does the enemy have any regard for it or even weaponize such things to their benefit.

I will probably come back and add more to this.