HiGetting a PCC takes some time and your mother’s trip is still more than a month away so I would suggest you start the application online from here. They need to verify everything at local police station so it’s good your father is there to followup.
In my case, parents are here in Canada so we applied online and locally in India we had my uncle follow up with local police.
Also, we submitted our PCC one month late than original deadline of 30 days so if it comes to that in your case, don’t worry, just apply as soon as possible right now and if you feel it won’t be here within 30 days then around day 22-25 or so, raise a web form so there is proof that you let IRCC know you’re still waiting and there are delays.
Thank you for your reply
I checked online on BLS document check list they are asking for original passport and I am worried if the passport does not come on time she may not be able to fly.