Hi Lawrence
Roth, Rothen and Koch are completely different surnames (at least today). Rochen and Rocher doesn't exist in Switzerland today.
Do you know her Heimatort (place of origin)? That would be the place with "von" in the records, while "zu" and "in" is the place of living.
The Heimatort was given by the father to his children at birth and to his wife at marriage. The Heimatort remains the same, even if they move to somewhere else. For example, I have a Heimatort where my family doesn't live anymore for about 100 years.
Birth, marriage and death are always registered at the place where it happened, but also in the Heimatort. So if you have her marriage record, it should name her Heimatort and there you should be able find her birth record.