A side note: Unfortunately, this game is another one I can't load (gives "internal error"). This has happened frequently in recent times and proves to be a nuisance to answer questions like this.
According to my understanding, this could be an error, but I'm not sure. The Royal Carriages are (in this turn) never played. All that gets played is the Dame Sylvia again and again. So when the playing of Dame Sylvia caused by the calling of RC#1 causes the Dame to be trashed, she is no longer in play.
Royal Carriage says:
Directly after you finish playing an Action card, if it's still in play, you may call this to replay that Action.
The question that I don't know the answer to is if the bold part is part of the trigger condition or of the trigger effect.
If it is part of the condition, then what happened was correct, as the RC#2 triggered successfully when the 'original' playing of Dame Sylvia finished and she was still in play. If it is part of the effect, then it was an error, as the effect of RC#2 would check if Dame Sylvia was in play and would find that she was not.
The game client seems to think it is part of the condition (I checked this with Mining Village and 2 Royal Carriages), but as I said, I'm not sure.