OK, thank you both, I didn't know they were that important. I will try them then. I also wonder is this "trust" concept an issue with the base game?
Trust is something that influences AI decisions even without Cossacks, I think. I only got Cossacks recently, so most of the time I've had EU4 I didn't have access to the diplomatic feedback/trust window, but I definitely got modifiers to AI willingness to join wars based on trust. Couldn't see what that trust was or have any way to influence it (aside from giving/not giving land in peace deals, I guess), but it was there. Usually not a big deal though.
It will always be easier to call an AI into a defensive war than an offensive one. It helps if you attack a rival of your AI ally, so maybe attack someone allied to your real target rather than the target themselves. i.e. maybe you're allied to Spain and want to attack Savoy, but Savoy is allied to France and Spain won't join you against them. If Spain and France are rivals, you may be able to get Spain to join vs. France, who will call Savoy in. Of course, you have to decide if having Spain is worth fighting France's alliance net. Or, if you can find a nation only allied to your target, attack them and drag your target in. If you don't want the penalties for taking land from a non-cobelligerent, force them to annul their alliances and attack them when the truce is up.