I think TWOW will depict her winning the Dothrakis differently.

The show is selling out to the "badass strong female" role trope they feel casual fans want to see.

You're 100% correct. I can't believe this comment is down here and up above is a comment suggesting Dany's going to be an archvillain. This sub is bizarre sometimes.

The entire purpose of Dany's arc in ADWD is to give her an "earned victory". She fucks up by making peace with the Meereenese nobility, realizes her error when she reopens the pits, and sheds her weakness by subjugating Drogon, flying off with him, and resolving herself while she wanders the Dothraki sea.

Casual fans of the show and the book alike hate this arc precisely because it's full of Dany making mistakes that they think are uncharacteristic of the "badass strong female" they want her to be, yet it's the one that forges her into someone actually capable of being a conqueror.

Also, if anyone doubts your prediction, it's worth noting that the Dothraki flee from Dany and Drogon, which is something that Dothraki never do.

He did not see her, though. The grass concealed her, and he was looking elsewhere. Dany followed his eyes, and there the shadow flew, with wings spread wide. The dragon was a mile off, and yet the scout stood frozen until his stallion began to whicker in fear. Then he woke as if from a dream, wheeled his mount about, and raced off through the tall grass at a gallop.

Dany watched him go. When the sound of his hooves had faded away to silence, she began to shout. She called until her voice was hoarse … and Drogon came, snorting plumes of smoke. The grass bowed down before him. Dany leapt onto his back. She stank of blood and sweat and fear, but none of that mattered. "To go forward I must go back," she said. Her bare legs tightened around the dragon's neck. She kicked him, and Drogon threw himself into the sky. Her whip was gone, so she used her hands and feet and turned him north by east, the way the scout had gone. Drogon went willingly enough; perhaps he smelled the rider's fear.