A lot of what Celene does is just normal for Orlesian politics. I tend to have a pretty poor opinion of nobles throughout Thedas; it is not just in Orlais that peasants, and in particularly the elves, are badly treated. The Chantry are also complicit in the way affairs are run. They criticise Tevinter, rightly, for sacrificing people in blood magic rituals in order to advance in power, yet overlook rulers like Celene doing exactly the same via assassins. It wasn't just Briala's family who died but every servant in the house in order to convince someone she was fit the rule. Gaspard would undoubtedly do just the same, as would any other noble in the "Game". It is noticeable that Celene actually marches against Halamshiral not just because of the play, but because the Divine insists she does something about the elf situation. So Justinia is just as culpable particularly as it is implied that this is quid pro quo for her doing something about the mage/Templar problem (which as yet has not broken out into outright rebellion).
If I'd been Celene, I'd have sent back the message that the Divine should jolly well sort out her own affairs and leave me to sort out mine in my own way. Fact is she had done something about it; she'd sent her personal assassin to sort out the problem. Presumably she knew it was going to take Briala a while to get there, so just needed to sit things out and defy Gaspard to openly attack her in the seat of her power. That was where Celene showed her greatest weakness in that she was too easily swayed from her original course; if she had genuinely felt that was the best solution to the problem, she should have stuck by her convictions. Quite why she need to go personally is also open to question; did she not have any loyal generals she could send on her behalf?
I never understood the timescale in Masked Empire either. How was it that Celene could get there so quickly that Briala arrived less than 24 hours before she did? Briala had already been gone several days before Celene set out, so even with enforced marches, Briala should still have got there sufficiently ahead of her to carry out her mission and get back to Halamshiral before the army arrived. If it was possible to travel there that quickly, why didn't she send Briala the same way, given how urgent her mission was? Instead Briala apparently had to take the normal amount of time, while Celene went express. So I feel there are elements of the plot in ME that are very contrived. Another was the whole business with Imshael and the eluvians.
In answer to the post though, as stated above, Celene is just being a noble, certainly no saint but no worse than any of the others. I'd like to abolish the "Game" but I doubt that would be an option.