Should i give her another shot even when she canceled on our date?

You act a bit strange to me. Of course it can happen that she suddenly has to cancel a date, especially if she is a busy person with a job, a family and extra activities/responsibilities. For some people their family or their religion (their job or their friends) are really important and you are just at the beginning of your relation so it is normal that she will put you on the second place. She did announce you one day before that she has to cancel and explained you why (I would have simply said family problems and not give more details). So, if you really like her, call her, if you have doubts don't, but if you over yze so much every situation and try to control everything you will never be able to have a long term relation.