Does it count only once
Yes.
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.
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1. What's the maximum dexterity bonus on your armor?
2. What's the maximum dexterity bonus on your shield?
3. Take the lower of lines 1 and 2.
4. What's your character's Dexterity bonus (or penalty) with no armor or shield?
5. Take the lower of lines 3 and 4.
The armor and shield aren't adding to your dex bonus, they are saying You can't be higher than this number.
The character normally has a dex bonus of +5 (from the ability score of 20).
The Hidden Soldier Armor has a max dex bonus of +3. So even though the character has a +5, the armor limits the bonus to +3.
The Basic Knight's shield has a max dex bonus of +4. That means while wearing the shield the character's max dex bonus is +4. But since its also wearing the Hidden Soldier Armor, the lower of the two maximums apply, and it is limited to a maximum of +3.
So even though the character has a dexterity of 20, its bonus while wearing this armor and shield is limited to +3.
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Ah, here we go.
Maximum Dex Bonus: You normally add your Dexterity modifier to your Armor Class (for both EAC and KAC), but it may be limited by your shield. Your shield’s maximum Dexterity bonus indicates how much of your Dexterity modifier you can add to your AC. Any excess Dexterity bonus doesn’t raise your AC further and is simply ignored for this purpose. If you are wearing armor with a maximum Dexterity bonus while wielding a shield with a maximum, you use the lower of the two values as your maximum.
Lets do an example.
Flarb the goblin solider has 18 dex, so a +4 modifier for dex.
With no armor worn, he has 14 EAC and KAC (10 base, +4 for dex).
Second Skin armor has a max dex of +5. Since Flarb's Dex is less than that, it provides no diminished to his dex bonus to armor, so wearing the Second Skin, he is at 15 EAC and 16 KAC (Since the armor is +1/+2, so EAC is 10 base + 4 dex + 1 armor, and KAC is 10 base + 4 dex, +2 armor).
If Flarb picks up a Riot shield, which has a max dex of +3, he now can only get +3 AC from his armor, since the +3 from the shield is worse than the +5 from his armor. With the shield, his EAC and KAC are 15 and 16. (EAC is 10 base + 3 from dex (max) + 1 from shield + 1 from armor, KAC is 10 base, +3 from dex (max), + 1 from shield, +2 from armor).
Now Flarb isn't very bright, so when he finds a Golemforged plating I and sees that the armor values on it are higher, he immediately puts it on, replacing the second skin, while still holding the shield. His new armor has a max dex bonus of only +0, which is worse than his shield, so he uses that now. His new EAC is 13, and his KAC is 16. (EAC is 10 base +0 dex +1 from shield +2 from armor, KAC is 10 base, +0 from dex, +1 from shield +5 from armor).
Flarb would be better off just wearing the second skin armor, but again, he's not very bright.