If I am interpreting this correctly, then according to this document issued by Manitoba Health on Jan 08 you are exempt from quarantining a second time if you did a quarantine in BC on arrival into the country. Section 2, paragraph (l) states:
(l) persons who have completed the period of isolation required under an emergency order made under the Quarantine Act (Canada) elsewhere in Canada, if they travel directly to Manitoba immediately after their required period of isolation ends.
https://www.gov.mb.ca/asset_library/en/proactive/2020_2021/orders-soe-selfisolation-01082021.pdf
Of course you would have to quarantine in BC according to the appropriate guidelines.
Just to confirm your situation, BOTH you and your Mother are traveling from Vietnam. Your Mother would quarantine with you in BC then she would continue to Winnipeg? Take note that is says she would not have to quarantine again IF she travels TO Manitoba IMMEDIATELY after her quarantine in BC. So no staying in BC after quarantine to do sightseeing.