New location, dog will not go to the bathroom

Question
Hello, first thank you for your services. I have a 2 year old black lab mix female. She is about 45 lbs.

History: I have had the dog since 6 weeks, I assure you she has never been abused, she has probably been hit once in her life. I have raised her since 6 weeks. She is spayed.

She is extremely intelligent, most things I never taught her, she picked up being housebroken on her own, (or from another dog), and I have never had on the leash, she never goes more than 20 feet from more.

She has lived in the same house with a large fenced back in back yard for 2 years with another female dog. She is very submissive. She cowers and runs from men, and any other dog besides the one she knows. Its very scary how submissive she is. I take her to the dog park, and she will hide under the bench, tail between the legs. She is honestly scared of the world.

I have relocated to apartment life 3 days ago, because of work means. I walk her constantly, but she still would not go to the bathroom. I cam e in last night and she had vomited on the floor, and was hiding in the corner, scared. Again, I have never hit this dog, she has never been abused, but she fears I am going to for some reason.

Nervous about her health, I took her back to my old house and let her use the bathroom, which she did. Extensively.

I know she was never on a leash, and now is, but the thing is I used to take her on day trips all the time (I travel locally for work), where she would never be on a leash, and she has never once used the bathroom outside my old backyard. (Except when she under 6 months old).

The other dog we were leaving with, was not abusive to her, but was definitely the dominant one. Female also. They would play all the time, like normal dogs, mine being the smaller one in the relationship. But any new dogs, she is scared of.

The way she acts, and her actions, how is she is just so aiming to please seems off sometimes.

Any advice on anything I can do, the bathroom being the more important obviously is greatly appreciated.

Answer
I think the only thing is more walks.  Let her stop and sniff posts or trees males might mark.  Females won't mark them, but often will squats and leave their mark.  Take treats along and if she does anything, praise her and give her treats.  Eventually she will have to go and if you reward her for it, its should get easier each time.