Please note: people's experience may not be reliable evidence you'll NEVER be asked for the required proof of funds, proof of place you'll stay, onward ticket.
I've never been asked . . but I always carry some funds, always have place to stay and have an onward ticket.
depending on country, it can take 3 months to prep for return travel so the dog probably wouldn't be going back with her. If you really want to know ask pet relocation companies and get a price off them.