Vancouver

BA can fly the two of you in Business on a few dates next month, eg 22nd.

BA and other airlines release far fewer business seats for redemption transatlantic E->W. You may need to pay on the return. However, things can change last minute, and non-availability now doesn’t mean non-availability with a few days to go.

Have you already checked if Premium Economy, or Economy, award seats are available for your return flights? If so, and you have enough Avios, you could do mixed-class return award bookings. In this case, it would have to be two separate return bookings if you and your mother fly back on different dates. You could ask BA to link them together so they would know you are travelling together in case of any disruption to your outbound flight.

No, it isn’t possible to combine award and cash flights in a single booking.

You might find some of the “Avios University” articles on HeadforPoints useful reading if you haven’t used points before, and there are lots of of helpful people here if you have any other questions.