14 week old puppy pooping in the crate at night and all over house?

My neighbor has a 14 week old female american pit bull terrier puppy that pees and poops all over her house and poops in her crate.
Please read ALL the info before responding.
Her crate is a small crate typically used for a cat so that there is not extra room for her to poop and she still does.
She will NOT yet walk on her leash,she stubbornly sits there and would rather be dragged than walked.Trust me I tried to help my neighbor with this to no avail.So walking her before bed to get things moving right now is not going to work.
She eats at 4pm and has nothing later than that.
She puts the pup in the yard for an hour to two before bed.
As far as discipline,I take the puppy once or twice a week and when she does pee or poop I shout a firm no and place her in the yard immediately.
Do you think that she may have a behavior problem?
I was thinking that she may have a food allergy that is causing her to have these issues(it is not always diarrhea,sometimes it’s hard) my neighbor feeds her Pedigree dog food,I know that she should be on puppy food but my neighbor does not want to buy 2 foods for her 2 dogs.
Please don’t be rude for it is not my dog and there is nothing I can do as far as forcing my neighbor to change her food.
She says that she brought her to the vet and they said that she’s fine.
Another thing,whether she’s at her owner’s house or visiting my home,there is another dog who you would think she would follow the lead from or learn from and she still does not.
I never said anything about the breed of my neighbor’s other dog or my dog.
The breeds have no baring on the situation.