A few comments here:
i) you made the choice to buy from a third party (presumably because they offered the flight for cheaper - though beware, most agents will charge you far more for added baggage than if you bought directly from EI) rather than from the airline. As such, queries regarding your ticket ahead of travel are supposed to be the responsibility of your agent - you've "paid" them to be your agent and middleman, rather than approaching the airline directly to do business with the airline yourself
ii) you already know the baggage allowance of your ticket - you say in post #2 that you have a 20kg allowance - so it seems rather irrelevant what "fare family" you have. Rather than buying a certain family from Aer Lingus, you instead bought a different product badged/presented in a different manner by a third party. Whether and if this equates to a "family" sold by EI is of little consequence to you. Fares sold on the GDS don't come as "fare families" - these kind of families are only sold directly by Aer Lingus themselves.
iii) if you have such difficulty with EI tickets bought from this agent - you refer to "massive issues" and having to claim back bag fees - perhaps it's time to consider buying travel directly from Aer Lingus, or from some other agent.