As far as I understand it, Vy is found at max. excess power which is not solely dependent on power required but also dependent on power available and the maximum difference between the two (i.e. the point of maximum distance between the two curves)
To complicate matters further, my instructor says that Vx is at Vmd! [Pretty sure this is wrong or at least the wrong way of looking at it as Vx is merely the speed for max. excess thrust as far as I understand]
The short answer is that you are correct in both cases.
A rather longer answer is provided below.
If we sketch the forces in a steady climb we will find that
The sine of the climb angle = Excess thrust / weight.
So for any given weight, we get max climb angle when flying at the speed at which excess thrust is a maximum. This speed is Vx.
And
Max ROC = Excess Power / Weight.
So for any given weight, we get max ROC when flying at the speed at which excess power is a maximum. This speed is Vy.
To find where Vx and Vy lie on our speed scale we need to look at how excess thrust and excess power vary with airspeed.
Props produce thrust by exerting a force on the air to accelerate the air backwards. The thrust produced is equal to the mass flow rate of air passing through the prop, multiplied by the acceleration given to that air. The acceleration is equal to the prop wash speed minus the aircraft TAS
For a simple fixed pitch prop and a normally aspirated piston-prop aircraft thrust is maximum before the start of the take-off run, when the air is given the maximum acceleration.
As the aircraft accelerates down the runway the difference between prop wash speed and TAS decreases, so the thrust decreases. So the thrust curve starts at a maximum when TAS is zero, then curves downwards as TAS increases.
Power available is thrust times TAS, so when we multiply the gradually decreasing thrust by the linearly increasing TAS throughout the speed range We get a hump-backed power available curve that starts at zero when TAS is zero, Curves up to a maximum at some intermediate speed, then curves back down to zero when prop wash speed equals TAS.
When we compare the downward curving thrust curve with the drag curve to get excess thrust, we find that the maximum occurs just below Vmp. The EASA ATPL exams assume that Vx prop is at about 1.1 Vs.
When we compare the hump-backed power available curve with the power required curve to get maximum excess power we find that this occurs at a speed that is slightly higher than Vmp. The EASA ATPL exams assume that Vy prop is Vmp.
So for a simple fixed pitch prop aircraft Vx is jaust below Vmp (about 1.1 Vs) and Vy is at or just above Vmp.
The use of variable pitch constant speed props extends the airspeed range over which thrust is close to maximum. This flattens out the top of the thrust curve, and moves Vx closer to Vmd. If we were able to maintain constant maximum thrust to Vmd and beyond, then Vx would be at Vmd.
The flatter thrust curve also extends the speed range over which power available is close to maximum. This also tends to increase the value of Vy.
So when OAA states that:
Vy is the same speed as Vmd for a propeller driven aircraft. They illustrate that Vy is found by drawing a vertical line down to the axis of TAS from the tangent of a line drawn from the origin of the axes of Power and TAS to the curve of Power Required. They also illustrate the same procedure for finding the Vmd and repeatedly state in the book and video that they are the same speed.
They are probably referring to a high performance aircraft with constant speed prop and turbocharger.