Hi Eva,
First of all, I'd like to express my sincere condolences. It must be quite overwhelming to deal with this situation right now.
If I understand correctly, you would come to the island with your own cat and then return to London with your mom's cat as well?
Some airlines allow pets in the cabin or in the hold, although it may be possible on certain routes only. I would check with the airlines first to make sure they are allowed. This
blog post may be helpful with choosing an airline.
Another way would be to use the ferry and the train/car, as they are more likely to accept pets on board. Some ferry operators between Ireland and the UK (e.g., Irish Ferries, Stena Line) allow pets, and you can travel with them as a pedestrian. Here's
more info about the routes.
Finally, here's more info on
pet travel requirements to the island of Ireland that you might find useful.
Let us know how it goes. :)
Antoine