The police were right; one cannot hold another's property hostage until payment is made, and it technically constitutes extortion
regardless of whether the payment is legally owed. Only if there was a good-faith dispute to ownership
of the property could it be held, but that basically went out the window when money was demanded for housing the dogs.
The computer analogy is not a good one because (1) if payment was due at the time of delivery, the purchase would not be complete so title would not be changed and it would simply constitute embezzlement, and (2) even if payment was not due after the time of delivery, it would constitute criminal fraud to take the computer when there was no intention to ever pay for it. I am not saying that this woman did not defraud you, nor am I saying that you should not report what happened for investigation, but I would be concerned about putting much hope into a positive outcome because it sounds like there could easily not be enough evidence for a criminal prosecution (which requires proof beyond a reasonable doubt). Civilly though, your case sounds pretty rock solid.
Is it ideal? No--and I am not going to sugar coat that. Because the law may be on your side, but you can't get blood from a turnip.
And yes, Tibetan Mastiffs are at least the second greatest breed in the world (second only to whatever type of dogs you rescue, I am sure