A few observations ;
Some home insurance policies do cover
contents temporarily removed from the house.
I am looking at a copy of Aviva's HOMECARE policy paragraph 14.
The dry cleaners might have their own commercial insurance that could cover this as a public liability claim.
A commercial policy might also include cover for
goods in trust as part of property insured.
I am looking at an AXA commercial policy that describes that exactly.
As far as wording a claim goes just keep it short and simple. e.g. we entrusted our property to you and it is now irreparably damaged and we hold you responsible.
As far as quantum goes I would be looking for the value of the goods here in Ireland as at the date of the loss.
I appreciate AndroidMan's argument at #11 above. However, I would argue that the "country of original purchase" price should not reduce the value of the claim. You are entitled to receive an indemnity.
Indemnity means that you are placed in the exact position that you enjoyed here at the time of the loss.
IMHO that would constitute the arguably true measure of your loss.
An analogy to complete the last point. I bought a new bicycle a few weeks ago. I paid €475 in a sale. The full value of the bicycle is nearer €750.
If my bicycle was stolen the replacement value I would claim would be €750 as that would be the presumed measure of my loss.
If the cleaners continue to prevaricate you can consider making a claim in the Small Claims Court.
The Small Claims Court's present limit is €2,000.
It only costs you a fee of €25, win or lose.
Who knows, if you are pushed this far there might be an additional element of upset at the sentimental loss and upset but I didn't suggest that

Link
https://www.courts.ie/small-claims-procedure