I think that if you are using autolayout and you want to change the position of a view, you need to be updating the constraints on the view instead of manually setting the center of a view. From the description it sounds like you are setting the center, but when the app next lays out the views (eg you drag another) it re-sets the center to whatever autolayout says it should be.
I'm not sure what the rest of your app looks like, but you may be able to find nearby views and add constraints to it, or you might prefer to just update the constraints of the dragged view and set the leading space and top space to the superview manually. If you've got a collection handy you could also clear all the constraints and then re-add them as you'd like to keep padding in between the views.
To set the constraints in code you can clear the constraints for the moved view and re-add them, or if you have a view in IB you can drag the constraints into code to create an outlet. Look at the removeConstraints and addConstraints methods to do it in code.
Lastly, if it works how you'd like without autolayout, you could try setting translatesAutoresizingMaskIntoConstraints = YES on the moved views, but be aware that may cause conflicts elsewhere.