The main reason your application was rejected was the purpose of the visit was poorly Described. Use the below as a model, I used it for my parents letter and good luck.
Letter of Invitation Sample:
Date, 201#
The Visa Officer
High Commission of Canada
Immigration Visa Section
City...
The purpose of visit is poorly describe on your invitation letter and that is why. I applied for super visa and it was approved, the invitation letter is also the key.
I guess it depends on where your visa application center is. Received PPR on October 3 sent passports by DHL on October 6 and received at visa application center October 9. Passports ready to be collected on October 30. Passports collected today with visa stamps.
I changed the effective date of my parents medical coverage to a later date as their applications are still under process. Do I need to send the new confirmation of coverage with new date to IRCC ?
For a family of 3, the LICO is $42100 for the most recent tax year. If you apply in 2023, your 2022 NOA or T4 should show a minimum of $42100 in your case. Did you meet the LICO?
Each country has its own processing time and if your mom applied from Bangladesh then processing her application can take more or less up to 272 days.
Super visa (parents and grandparents)
Bangladesh
272 days