The Tal Shiar and Obsidian Order have worked together in the past, not necessarily the Union and Star Empire and definately not the Republic and the Union. It's entirely possibly that your average Romulan or Cardassian doesn't even know the Battle of the Omarion Nebula even happened.
And as to how the Klingons would view a Cardassian/Romulan alliance; We're talking about a race that believe "Once it is up, a Klingon never lets down their guard, and a Klingon's guard is up from the first moment he draws breath".
Think about it, the Martok-Changling helped push it, yes, but the Klingons believed that just because the Cardassian civilians overthrew the Central Command after centuries of military rule, they had to have help from the Dominion and Changlings and used that as an excuse to attack the Cardassians.
The Fed-RR-Klingon triangle can be accepted to a degree because it keeps the Republic divided and weak while giving the Klingons hostages in the form of KDF-Roms to ensure good behavior. Bring the Cardassians - an enemy of the Klingons - into the equation and suddenly you've got two 'former' enemies and one current enemy all working together to some degree. Klingons may be many things, but foolish Klingons do not live long and only a fool wouldn't consider that a potential threat to the Empire. The Klingons are the type to consider the ability to be a threat equal to the fact of being a threat; as long as the Republic is divided between them and the Federation and they can control some of the flow of resources, the Republic is not a threat. Ally the Cardassian Union and Republic, increase the flow of resources between both groups in a way that the Empire can't control... they both become a threat.
"A hand that remains closed ceases to be a hand." - The Prophets, 'Of Bajor'.
"A discount that is not applied is not a discount." - regarding the 2014 Breen Ship Situation.