Will my kitten be ok if I shut her in the bathroom at night and when I'm not home?

I've had her about 3 days now, and I don't really want to lock her away. I want to be able to trust her, but she has diarrhea due to her shelter switching her food from one bad brand to another multiple times. She was only on the last brand for a day before I switched her to a good quality brand. She knows how to use the litter box, and will happily go when prompted, but will continue to poop in all corners of my apartment when not closely monitored. She can go pee all by herself though, so I don't think it's a litter issue. My boyfriend and I are very tired of scrubbing the carpet and we are also renting, so I can't afford to have it ruined. She also liked to leave the room and cry loudly all the way back to one of us. She will do it about every 15-20 minutes all night long. I would be more able to deal with this issue if I could trust her not to poo everywhere. The bathroom is the only place in the apartment that had a door that will stay closed, it's not a huge room but moderately sized. She has food, water, her litter box ( that had been there since day one), a box with blankets to sleep in, a dim nightlight so it isn't too dark at night (I leave the light on while I'm at work) the fan circulates constantly, and also a towel in the bath tub in case she wants to be in there. I guess what I'm asking is, will she be alright if I have to shut her away when she isn't under supervision, at least until she can control her bowels?