Yes and no about Emerald - a lot of the routes are ones deemed too thin for an A320, and EI's publicly stated intention when creating EIR was to grow markets to a point.where EI could take them over and provide additional frequency on some routes - a lot of the aim is transatlantic feed and that's directly a requirement of EI.
You have to remember the BE brand was on these BHD routes way back, it's really well known here and they're basically only trying to take back the same business they had previously - IAG came in new to the routes as a result of BE going bust. Also BE historically had for instance 7x daily rotations BHD to BHX and MAN, so adding what they have now + EIR really only adds up to the same or less frequency/capacity - it's not perhaps the dog fight it's being made out to be.