Woodworker here. Building with "wet" wood will always result in some wood movement. For exterior applications, wood with around 9-14% moisture is reasonable. For interior applications, more like 6-8%. You can get moisture measuring devices to give you an exact reading.

Green treated wood is not great as most box stores will not allow it to dry properly before putting it up for sale. You can plan for this will corner bracing and such, but it will move on you if too wet. You can find stacks in the lumber yards that are drier than others which can help. Another option for exterior applications is to use kiln dried wood such as cedar and then apply a good sealer to it. If you really want to use the green treated stuff and it's too wet, stack it with shims between the layers and allow it to air dry until you get to the desired moisture. That should minimize the movement after building with it.

There is a good article here.