Ulf Markham is still alive in Jerry Pournelle's and SM Stirling's last Man-Kzin Wars story and is killed in Poul Anderson's first Man-Kzin Wars story. Therefore, all the Pournelle-Stirling stories are set before all the Anderson stories. Simple.
In "Warriors," Larry Niven introduced the kzinti, thus creating a Man-Kzin Wars period in his Known Space future history which also features several human colony planets including Wunderland in the Alpha Centauri system.
In "The Children's Hour," Jerry Pournelle and SM Stirling introduced Harald's Terran Bar in Munchen on Wunderland during the kzinti occupation.
In "Iron," Poul Anderson introduced Robert and Dorcas Saxtorph who fly from Sol to Alpha Centauri to negotiate with Commissioner Markham of the Interworld Commission after the kzinti occupation.
In "Inconstant Star," Anderson introduces Tyra Nordbo who meets with Robert Saxtorph in Harald's Terran Bar.
"The Children's Hour" and "The Asteroid Queen" by Pournelle and Stirling show us Markham before he meets Saxtorph. Their "In The Hall of the Mountain King" shows us Tyra before she meets Saxtorph.
And I think I have got that right.
"'...[the kzinti] did invent the gravity polarizer.'" (The Man-Kzin Wars, p. 80)
This was said before it was learned that the kzinti got all their space technology from another race. Many, though not all, of the apparent contradictions in a series can be ironed out by reflecting that most statements are made from particular points of view. In Anderson's Technic History, are the Merseians mammals? See here.
When Saxtorph visits Harald's Terran Bar, it no longer displays a "humans only" sign. Saxtorph reflects:
"Mustn't offend potential customers or, God forbid, local idealists." (Man-Kzin Wars III, p. 175)
Those who object to a "humans only" sign are to be disparaged as "idealists"? I would experience a certain amount of social friction if I were to meet some of Anderson's characters.
There will be more but not tonight.