Urgent Advice Needed

[CreakyKnees01]

My Dd took on a 5 month old lurcher type dog about 2yrs ago. The dog means everything to her and she has poured her heart, soul and finances into this dog.
However, there have been problems with behaviour since day 1.
It's not good with other dogs, it still messes in the house, it's very destructive.
Dd has really tried hard with training, it gets lots of exercise, attention and has every toy you could think of.
Whilst she was living with me , the dog bit my younger Dd and went to bite me when I was trying to stop her digging up my lawn.
It's now got to the point where the dog is making Dds life miserable and she has enquired about rehoming.
Tonight she has phoned me very upset because the dog has bitten her again.
I'm I right in thinking the dog is not going to be rehomed with a bite history and it would be safer and kinder to get the dog PTS.
This is breaking Dds heart but I don't know what else to do.
Any suggestions gratefully received

From your update about where the dog came from, it just sounds like she's unsocialised and badly trained (rather than being unpredictable) and as your DD is young and unexperienced, she's in way over her head.

I don't think this dog needs to be PTS. I think it needs to go to an experienced home with someone who has experience of sighthounds and who has the knowledge to train her properly.

I feel inclined to agree here, OP. It also sounds to me as though the dog isn't really getting enough stimulation/exercise, before being taught to "switch off".

We take our dog out for an hour's walk first thing, and then she goes back to her crate for a good two hours to decompress and settle down. She's learnt to sleep and calm down during this time. She's out in the garden for a short burst at lunch, then has another half-hour walk before her dinner, and then it's back in the crate for at least an hour, if not two. Dogs need to learn to switch off so that they're not still wired and they're not overly stressed. Is this something your dd has tried? It could help if not. Wishing her lots of luck!