Hey ClassyGentleman,
In order for the other clients to know how to adjust the Aim Offset, your Character or Controller will have to replicate the rotation values (like what you are doing in your Animation Blueprint) but instead, do it in your Character / Controller and make sure it is the Authority setting the Aim Offset values.
Then, in your Animation Blueprint, you’ll just get a reference to the Character and get those values directly and set them to the values needed in the Animation Blueprint to adjust the Aim Offset Blueprint.