I'm very sorry for what your daughter has been through.
Essentially in law a dog is considered a possession like any other household item (a sofa, a fridge for example).
I appreciate that this sounds bizarre, but it's the case as the law stands currently.
Disputes over dog ownership are therefore disputes over property, and the burden of proof falls on the person claiming ownership to show that the dog is in fact theirs.
It is a matter for a district judge in a small claims (county) court to decide the outcome of any dispute under the Torts (Interference With Goods) Act 1977, where a declaration of ownership can be made.
Acting quickly is paramount to the success of any claim, so I suggest you don't waste any time getting on with it.
There is a specialist firm who may be able to assist here, they offer a fixed fee 20 minute consultation for £60:
I trust that this assists?