Debt Recovery Plus (DRP) is a third-party debt collector, not a law firm. They cannot take you to court. Their letters are designed to pressure the low-hanging fruit on the gullible tree into paying, but they carry no legal weight.
APCOA, the parking operator, could theoretically issue a claim in the English County Court. But since you live in Ireland, they would need to serve you out of jurisdiction under Civil Procedure Rules Part 6. That involves much extra cost, procedural hurdles, and justification for why England is the appropriate forum. For a £100 parking charge, this is not going to happen. APCOA has no known history of pursuing UK, never mind Irish residents, through the courts for single PCNs.
If the rental company (Alamo) received the original notice, they may have named you as the hirer under Schedule 4 of the Protection of Freedoms Act 2012. But if you were never served the original PCN or Notice to Hirer, you were denied the opportunity to appeal, which undermines any claim of procedural fairness.
In short: no court claim has been issued, APCOA has no jurisdiction in Ireland, and ignoring DRP is safe in your or any case. You were not properly notified, the alleged contravention is minor, and APCOA simply doesn’t litigate single PCNs—especially cross-border.