You say she poops almost as soon as you close the door…. have you tried doing very short incriments? for example... start with her in the crate and don't shut the door at all. praise her. if she starts to squat to poo - whisk her outside.
then start closing the door - first for 10 seconds, then 30 seconds, then a minute, and so on. Try this on the weekend when you're home and can devote some time to it. praise her lavishly when she doesn't poo in it.
just out of curiousity, what type of crate do you have? as insignificant as it sounds, it may be an issue for your pup. I favor the all over wire crates, so I can see in, and the pup can see out. I do not cover the crate. and then again, some other dogs prefer the plastic vari-kennel kind.
my dog never pooped in his crate, but at 11 wks old, did have a couple pee accidents in there. be sure to clean the crate really well, and keep the space available small, yet large enough for her to stand, turn around, and lay down comfortably. it should be like a cozy den, like a small nest. not enough room for her to poo and then lay down away from the poo.