The gusty section can be tough to navigate but the following GIF will give you an idea of how to get through it:
The foam at the beginning of the second screen can be cleared with some easy egg shots that act very consistently. The first egg shot is a neutral that's fired as soon as Yoshi comes out of the pipe. The second shot is a neutral that's fired immediately after Yoshi runs off the foam he just shot through. The third shot needs to be angled straight ahead but will generally carve out the pattern you see in the following GIF. The fourth shot is a neutral that is fired as Yoshi crosses the second-to-last patch of foam that remains from what he just shot.
Facing right when grabbing the baby mario star will give you a boost to the left (see IL) but if the boost makes you scrape the wall you will lose time. Make sure to hold Y to run with super baby mario. Jumping on downward slopes increases super baby mario's speed.