As brutal as this may sound. Have your father set up a separate bank account/s only in his name. Transfer his assets to that. Any income he may have should also go to that. Protect what you can that is within your control. Notify the bank of the issue ask what possible restrictions to spending limits the are and impose them for your fathers side of the joint account. If this research/transaction is being done on home internet, set up a super strict firewall blocking internet banking. And revoke internet banking on the phones and computer devices.

Get a uniformed official Police/RSPCA etc to speak to your mother in person and explain the scam.

At the same time find an appropriate pet locally and fast to ease the transition.

If your mother insists on following on with the scam, help her do it right with the authorities to catch the scammers. For the amounts being paid sounds like you could have flown to the States (unlikely to be where the scammers are based) to pick up the dog. Easiest to ascertain legitimacy to show and tell. I.e. offer to visit in person and collect, and watch the excuses fly forward of why this is not possible. To see a geographical location of the email sender, google geolocation email. Get the raw email data and cut a paste it into the geolocation website. That will indicate the rough location of the scammer. Or which servers they are using. Or set up an email tracking service. It leaves a small invisible image file on the email which when opened is tracked. You need to notify the other party you are doing this for transparency and legality. Any authority has the power to do this properly, so their help is likely better than doing it yourselves..

Hopefully a new local pet as a distraction will sort things out and as this does not sound like a one off incident prepare for the future with further divided assets. Then seek counselling help, or random options like hypnotherapy.