It sounds to me like you may have a major misinterpretation going on. I realize some of this may be obvious but for the sake of more certainty and clarity:
Dex bonus: a character gets this bonus to their AC (subject to the limit of the max dex bonus). The character gets this - it doesn't add to the armor.
Max dex bonus: from CRB, page 196
Maximum Dex Bonus: You normally add your Dexterity modifier to your Armor Class (for both EAC and KAC), but it’s limited by your armor. Your armor’s maximum Dexterity bonus indicates how much of your Dexterity modifier you
can add to AC. Any excess Dexterity doesn’t raise your AC further and is simply ignored for this purpose.
The idea here is that it's hard to be agile in heavy armor. So no matter how agile you are, the armor limits your dodging. If you have an armor with a max dex of +3, then you'll never get more than a +3 from your dex bonus. But if your dex bonus is only +1, then you only get +1.
If you have armor with a max dex of +3 and a shield with a max dex of +4, then your max dex bonus is +3 - the more limiting of the two.
There's no counting "twice" since the dex bonus adds to the *character*, not the armor/shield.