You can not mix and match tech generations (X2, X1, and non-X) between the support DD and the scout. For example, the Federation could not have a DDX and GSC (or a GSX and a DD).
When targeting an ESM ship, treat the SC and support ship as a single unit for targeting purposes. For example, if the SC has 30DF and the DD 20DF, the combined "unit" is targeted as a 50DF unit. If you can via special attacks (directed damage, maulers, etc.), generate that 50 points of effective damage, then both ships are destroyed. If you can't generate the full damage, you'd need to use the less effective partial directed damage attack or target some other unit.