Идти and ходить (мама шла/ мама ходила) belong to a particular set of verbs called the verbs of motion. English has the verb "to go" to convey the idea of travel (among other definitions). There is a large group, and I suggest googling "Russian verbs of motion." For this exercise, understanding that all verbs of motion come in pairs. These pairs convey whether or not the subject has gone from point A to point B or from point A to point B then back to A. In other words did the person come back or not. This is a strange distinction for English speakers, but it is very pertinent to the meaning of the sentence in Russian. The use of ходить (ходила - conjugated into the past tense and agreeing with a female subject) means that the subject made repeated regular trips to work in the past. I really suggest googling this and doing some research. Knowing a little theory in this subject helps.
I think this is the answer: 'в' is generally used for a place you enter, and 'на' is used for outside-type places. I have a short list of places that take 'на' when you'd perhaps expect to use 'в': на заводу (to the factory), на консерту (to the concert), and of course на работу.
I’m not seeing a distinction between verbs in the past that are completed vs. ongoing. In French I believe we called that “passé composé” and “imparfait”. In English there’s a difference between “mom was going to work” and “mom went to work” but both are accepted as translations here?