Using 2 June as the return:

Holy... I-class, completely inflexible, comes in at £2,700. Not cheap but not shocking.

R, the next fare up, comes in at £7686 in ITA. NOT a typo.

As Ldnn1 has suggested, there may be a changeable I-bucket fare that is less painful but I don't have that kind of access.

You could do an ex-DUB the weekend before, so your family is basically going on a day trip rather than schlepping them through airports with luggage and tight connections, then return to the UK in A with a longer lead time - NOT 'I' as the restrictive UK fare would govern the whole trip. That comes in at about £3k.