Do you mean rotating the target vector around another vector ?
If so use your another vector as the rotation axis and call the D3DXMatrixRotationAxis() method to create a rotation matrix wich rotates your target vector around that another vector.
The function is simple to use, you provide it with the following parameters :
D3DXMatrix* pOut - The resulting rotation matrix
D3DXVECTOR3* pVec - Rotation axis (the axis vector which is the vector you want to rotate your target vector around)
FLOAT angle - Rotation angle

Now you can use the D3DXVec3TransformCoord() method as you did before to rotate your target vector as needed providing the method with the rotation matrix created before.

The rotation is defined around an axis (not around a point). So, for rotating m_target around m_position, I understand that you desire to rotate m_target around an axis that passes by the origin and by m_position. Is it really it what you want? Perhaps you would like to rotate m_target around a vertical axis that passes by m_position.

In the first case, you could do:

D3DXMatrixRotationAxis(&m_tempMatrix,&m_position ,theta); // Transform m_target by m_tempMatrixD3DXVec3TransformCoord(&m_target, &m_target, &m_tempMatrix);

In the second case, you could do:

// I suppose the y-axis is your vertical axisD3DXMatrixRotationY(&m_tempMatrix,theta); // Transform m_target by m_tempMatrixD3DXVec3TransformCoord(&m_target, &m_target, &m_tempMatrix);

If x = 0 then no rotation will take place.
The angle provided is the angle of rotation of the current object / vertex
which means if x = 90 the object / vertex will be rotated 90 degrees from its current rotation state.

Also note that the angle your provide needs to be in radians.
If you want to rotate in x degrees use the macro D3DXToRadian(x) to get the rotation angle in radians.