Sansouci,
Sorry hun, would not think you will get an upgrade as such flights are usually full. BA only fly once a day to Vancouver I believe and get in quite late in the day. Wondering why you did not therefore choose Air Canada instead?.
If your two year old wears a nappy change it before you board the aircraft. This will save you some hassle.
Take full advantage of the early boarding you will be offered at the departure gate.
Pushchair (if used) can be taken up to the gate and BA staff will tag it for you.
Do not take anything really tiny for the children to play with; if its dropped you'll probably not see it again
Portable DVD player is good, some batteries have several hours of life.
Flight back to UK should be easier as they should sleep most of the way.
When do you leave for Vancouver, you may be able to choose your seats online. BA's website has this facility.
Unfortunately you will not be able to take advantage of the online check in they have in use because of the children.
Make sure you have all the documentation you require to hand well before setting off.
Vancouver is a nice modern airport and you won't have to walk miles to get to immigration either. If memory serves me correctly the lugguge carousel is immediately behind immigration. You will need some money (I think its $3 in notes or thereabouts)to get the luggage trolley.