Well, if it's turning, the roll servo is probably in the wing. And if it's nosing down, the pitch servo is somewhere in the fuselage. Think you broke two shear pins?
I don't think the servo is mounted in the wing on the RV-12, check your manual for the proper location.
The Dynon EFIS (Both the D100/180 and the Skyview) has an AP test mode that you can run on the ground. Give that a try and you will find out pretty quickly if you have a broken sheer pin.
Order the sheer pin from Dynon, if needed. It will come with instructions and a new cotter pin. You will need to get some Loctite from your local auto parts place. The instructions will tell you which color to get.
To replace the pin, you remove the cotter pin on the servo arm and the castle nut. Do not remove the servo or the rod connecting it to the flight controls.
Remove the head of the old sheer pin, if it is still in there. (Mine fell out.)
Put some Loctite on the new pin, place the servo arm back on the servo, and screw it in an empty hole. (There are three and one is probably taken by the broken pin.) DO NOT tighten the pin. It should go in until it seats, that's all. If you tighten it, it will probably snap the first time the AP is engaged.
Put the washer, castle nut, and cotter pin back on.
With that done, you will need to calibrate your AP again. Check the Dynon manual for how to do that.
One other thing, I went through a few of the pins when I was a Beta tester for Dynon. Check with Dynon for the proper setup for your RV-12. With the correct setting (and installation. DO NOT over tighten the pin!), you shouldn't have any more issues.