Welcome to the Wefugees Community and thank you for reaching out to us.
It is always very difficult to judge on or to predict an asylum case's chance - especially without knowing the whole story. At the end, it will be essential that the applicant is explaining her/his reasons for the application very well and plausible to the BAMF staff at the interview ("Anhörung"). Based on the statements made here, the caseworker will decide to grant international protection or not. The applicant may support his/her explanations with proofs as pictures, letters etc. I would highly recommend to consult a "Verfahrensberatung" prior the interview - experts in this field will help with the preparations.
About the relocation in Germany: If her sons are already older than 18 years and there are no urgent reasons why the family needs to be together (i.e. one member needs to take care of another family member), it could get difficult to convince the authorites to agree on the relocation. However, people are usually only restricted to stay in their initial place for maximum 3 years (Wohnsitzauflage) and can move within Germany afterwards. This will be easier if people are not depending on social money and generate their own income.
Do you agree dear @mbeon-fardeen and/or is there anything you may want to add?
In any case, please don't hesitate to get back to us with any further questions.
All the best,