Итого, обладателям действующих кипрских ME2/3 (yellow slip - на карте должно быть FAMILY MEMBER EU 2004/38/EC art 10 (внж) или art 20(пмж)) не требуется шенгенская/ирландская виза для посещения Шенгена/Ирландии, а так же присутствие члена семьи ЕС/сертификата о браке/прочие дополнительные документы:

"Possession of a residence card issued under Article 10 and Article 20 of Directive 2004/38/EC (124) constitutes sufficient proof that the holder of that card is a family member of an EU citizen (125). The residence card has visa-exempting effect in every Member State, including in the EU citizen’s Member State of nationality (126) and regardless of the participation of the issuing or visited Member State in the Schengen area without controls at internal borders (the Schengen area) (127)."

Commission Notice – Guidance on the right of free movement of EU citizens and their families
https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A52023XC01392