Aeroskid - EI management will have to work within the parameters they are given by their owners IAG. IAG will control fleet purchase decisions, slots, capital investments and purchasing. They will leave the running of EI to the management within agreed business plans. There won't be the opportunity to source aircraft elsewhere avoiding IAG agreement.
It is worth remembering there are benefits to this. Take A350s for example. If for example growth didn't materialise quick enough, IAG could juggle delivery slots between the carriers in the group to better use them. I.E. create opportunities for internal deferral of deliveries etc. It works both ways can save empty seats and carrying the cost of premature deliveries for a carrier. Perhaps it could mean season movement of aircraft - EI on North Atlantic in the summer and IB on South Atlantic in the winter. Who knows.
You are right to see that this creates competition between carriers on costs and revenue. The group are also using it as a way to move management between carriers. e.g. CEO of Vuelling moving to BA, CEO of IAG Cargo becoming CFO of BA, IB CFO becoming CEO of Vuelling (may have the last one wrong).
I'm sure DUB will become an important hub. It can cover UK regions to USA cheaper than via LHR. Also it is a strategic hedge against UK runway decision or lack of it. Remember WW is a very smart guy regardless of whether people like him or not.