Yukino is a weird one,the ability itself is the ability to Shapeshift into any animal,be it fictional or real. The powers come from Yuuri's side,but its not that Yuuri dosnt have the powers or chooses not to use them.

It's because for the Katsuki Family,their powers are relatively Dormant,they have them,they just dont know.

Sometimes Dormant powers can be woken by a Sudden,Fast Jolt of Power,or a Really REALLY bad hit to the head.

For Yuki,it was because Natalya chucked a Baseball going at HighSpeed that gave her a 3-day Concussion. (So... Both?)

As for Dragons... that would be Yukino subconsciously going for Dragons.