My gear:

dawnguard light helm
leather armor
dawnguard light gauntlets
dawnguard light boots
twin dawnguard axes
dawnguard heavy shield


Wen I have the two axes equipped, my AR is 170, when I have an axe and shield, my AR is 166. WTF?

well seeing as how you're wearing all light armor and your shield is heavy im going to assume that you are using light armor as a main skill and you have the perk in light armor that gives you a defense bonus (25% i think) when wearing all light armor, and since you put on the heavy armor shield it takes that bonus away ultimately lowering your armor rating.

Im sure thats the problem.

Get a light armor shield and i bet your armor rating will increase instead of dropping.

The shield has nothing to do with the all light or heavy bonus. It is only the armor, boots, gloves and helm that matters.

There is one light armor perk that gives you a bonus if you are using all light armor. Seems like there is one further along too that gives another bonus if it is all a matching set.

I figured the shield counted into that too. Doesn't it?

Anthropoid and Sentinel - I agree. That's undoubtedly the root of the problem.