What a mess. Details are missing. Difficult to tell who did what wrong. First of all, it was Air Canada's responsibility to re-book you on the next available flight in business. You went with United which is fine, but they must have re-booked you in coach, perhaps why they were able to find you a seat out more quickly? Did you not check your reservation after the ticket was re-issued? You should have asked to be re-routed on UA metal - that would have been a lot easier!
So now you got to travel and you didn't check your BPs? That it was coach across the Atlantic? Then you called mid-itinerary to get it fixed? A LOT can go wrong here and I am not surprised this got messed up in a bad way. Having a reservation does not mean the same as having a ticket. Did both of you have a ticket for the EI flight?
UA should refund the difference in miles between coach and business.
If you had a business-class ticket (not a reservation) then EI should provide downgrade compensation based on EC reg 261
If you had a ticket for the flight and EI refused transportation then EI should provide compensation for that based on EC reg 261
If you issues with your bags, that is also on EI to fix