The MPs from Ireland could, and absolutely did, write and pass laws. Those laws were just as binding on England, Scotland and Wales just as much as Ireland, and also the empire at large.
MEPs cannot write a single law. Only the unelected Commission can, and the Commission is also the body that passes laws. Complete opposite of separation of powers.
Ireland sought its independence so they could vote it away in a scant few decades, really?
The MPs would propose laws and get votes on them, but if they opposed a law, they would be overruled by England who had more votes. In the EU council they get a veto vote
MEPs can propose laws to the EU commission to prepare and bring to vote. The Commission cannot come up with laws on its own.
the commission is NOT the body that passes laws - that is the EU parliament (analgous to US Congress) and the EU council (analogous to the US senate) that does that
Ireland has more independence and power in the EU than it ever had under the English
The main benefit to Ireland of EU membership was close union with the UK without having to be seen as united with the UK.