We flew a dog and two cats from the States, and it was breathlessly expensive!!! But our dog is quite heavy, and they usually charge by weight. I would suggest that you look at the web sites of various airlines, they usually post info about costs on there. Also, the quarantine thing has been lifted, but not sure that your mum would have to do that from within the EU anyway.
she's trying to get rid of dogs, not add more! She's got 2 at the moment and realises it was a mistake ... a friend of hers (in England) wants to have one of them, but I doubt she'd be prepared to pay astronomical sums to have him transported back. She doesn't want to send him to an italian dogs' home because she fears the pampered pooch will end up chained outside a farm somewhere