Why is that woman sweat-dropping? Is it because of those ears?

Why is the woman even covering the child's eyes?

What's she censoring here?

"Don't look at the depressed umamusume that uses the first train car to emulate being ahead of the pack"?

It's because Suzuka is behaving unusually (up against the front of the first car looking through the window with wiggling ears), and it's standard fare for all mothers in Japan to cover their children's eyes, turn away, and sweatdrop when anyone behaves against social norms.