V2??? No!!!
JIC, you have it all basically correct, if one assumes thrust is constant (which it may be close to true for an old turbo jet, not that close for a turboprop). Usually the flight manual or performance manual publishes Vy, speed for maximum rate of climb (all engines). Typically though, one climbs at a higher speed, computed to minimize the cost of the flight.
Vx (all engines) is rarely published, and I've never heard anyone use it although I can imagine some scenarios where it would be useful. If the published holding speeds are in fact Vmd, and not some higher speed to aid in aircraft handling, then I'd say this is the Vx speed for that weight.
What one may be able to determine is Vx for one engine inop. Typically, Vfs, the final segment climb speed, is chosen to be the maximum angle climb speed for one engine inop, to allow the best climb gradient.
How do you find Vx and Vy on the ATR? Some elaborate flight tests would get you the answers.
Vx and Vy mean the same for big or small aircraft, regardless of the power plant. Keep googling, and reading.