when you want to get a turret but the enemy anivia is under it

Because Poppy is a terrible engage tank.

Her "engage" is her pressing W to speed up and then press E on a guy. The guy you E'd most likely is not going to get stunned if say you were sieging down a lane, and your W has a ~~500 ~~apparently it's actually a pathetic 425 cast range which is below most champions attack ranges. And you just used your ult to remove everyone from the fight. Even if you didn't, it's still complete garbage since Poppy's ult renders all targets untargetable meaning follow up wombo comboing just does not exist. The best engage you could possibly do is either to use your passive+iceborn/deadmans to slow a guy (which is a really bad engage unless your team as a whole is that ahead that a mere slow is enough to get people downed) or to E in and then maybe ult 4 people, but again that's only if your team is THAT ahead of the other that the movement is the only benefactor.

What Poppy is good for, is countering enemy engage. her W, E and Q are all great at punishing over aggression. You can block a j4 flag drag, a lee sin at any part of his insec combo, a thresh who landed his hook and is using death leap, an amum, Kayn coming through a wall is just an easy wall pin, darius and nasus the slowwalker is an easy ult target, etc. Her peel is actually great and easy to use, it's just she sucks at engage.