Find direction from current direction rotated by angle

Based on your image, there are multiple solutions to your problem:

This example is the pure Vector3 approach, using Vector3.Reflect(). Calculate the reflection of the first ball's heading against the normal of a plane (symbolic, not literal) formed passing through both balls:

 // The heading of ball1 (e.g. its current velocity
 Vector3 ball1Heading = ball1Rigidbody.velocity;

 // The vector from ball1 to ball2
 Vector3 ball1To2Dir = (ball2Transform.position - ball1Transform.position);

 // A perpendicular vector to the previous two,
 // unable to be found if heading and from-to are parallel
 Vector3 perpendicular = Vector3.Cross(ball1Heading, ball1To2Dir);

 // The reflection normal, obtained utilizing the new perpendicular vector
 Vector3 reflectionNormal = Vector3.Cross(ball1To2Dir, perpendicular).normalized;

 // The reflection of ball1's heading against the reflectionNormal
 Vector3 reflectedHeading = Vector3.Reflect(ball1Heading, reflectionNormal);