I understand well what you mean with the need to check off this box but :
any idea why when the box is checked for all 3 mods the game won't load the saved games even it is just after saving ? In this case all required mods are loaded in their required version but the game doesn't take it.
To be clear, by "required version" I also mean time/date stamps. As in, if you built the mod and started a game with it, then went into the mod and changed anything (like those flags) and built it again, then even though the new build will have the same version number as the old one, the game won't see it as being the same entity. Although, I've never heard of it giving that sort of explicit "no" in that situation; usually it just breaks miserably in practice.
In my configuration all units, buildings and resources are in the main mod. The secondary mods only have entries specific to DLC civs for units whose classes are defined in the main mod.
That's possibly related to a separate issue I've experienced. Civ has a serious problem with cross-compatibility; if you add a new XML table in one mod and add elements to that table in another mod, then it won't accept it. I really hope the devs get around to adding the mod dependency structure that ModBuddy already has interfaces for, because my own mods REALLY could use that. Similarly, if you've got something like you've described (where an Update command in mod A modifies a Row element in mod B), it might not work correctly if the mods are loading in the wrong order. (Although, it seems that SQL always parses after all XML, so if you move the Update into an SQL entry it might work better.)
So in relation to the previous issue, it's possible that the load order mattered, and that even though you're loading the same three mods again, you might not be loading them in the same order as before, which could cause problems where there are now some elements failing to add/modify. Now, we've had arguments on what exactly controls the load order; in my experience, the game handles it through the order you turned on those little green circles in the Browse Mods menu, and you can check load order through a Lua command in FireTuner (or through editing a version of the setup menu windows, like I've done for my own mod).
This sort of thing is especially problematic when you alter the "base" mod without rebuilding the ones that depend on it, but in my experience if you go into that menu and turn every mod off, then re-enable them in the right order, it seems to work okay. Obviously, if you don't remember the order from the first time it could be a problem. (Hmm, doesn't the Load menu allow you to click on that one spot on the left to see which mods were loaded? Try them in that order.)