Her greyhound is causing her sleepless nights

I think the first step is to take him to the vet and make sure there's no physical cause.

Sounds like it is food related and too much in quantity - lots of kibble seem cheap to buy but full of “fillers”. My sighthounds are on good quality kibble and produce two poos a day. Quantity wise they don’t have much to eat. They don’t do well on chicken based food either which is quite common. They are on a fish based and grain free kibble with a small amount of grain free tin each. A 12kg sack lasts my 3dogs a month. There is a good website “all about dog food” which gives ratings.

I would recommend raw food (my Rosie has Bella&Duke frozen, but there are many others ) and rethink what time she feeds him. Perhaps she also feeds him too much? If he was not clean in his kennel or toilet trained when she got him, it’s back to basics.Let out in the garden immediately after each meal to encourage him to do his business.
Rosie is fed about 4.30 and always has a walk before bedtime - round the block on the lead - and always pees at least twice and poos so I know she will be OK. If this boy is asking to go out that is in itself a good sign, but course he may just enjoy having a nosey round the garden, perhaps hearing cats, foxes or hedgehogs.
You could talk to the rescue kennel where you got him or if you PM me I will give you the details of the kennels Rosie came from, they are really kind and helpful. I hope it settles down soon, from my experience ( Rosie is my fifth greyhound) they usually sleep about 25 hours a day!

He has the most lovely temperament. He was quite underweight last year and the vet advised her to increase his food intake. He has put on some weight and looks better, but the downside is this nightly problem. It is good he ‘asks’ to go out, and he does do his business every single time she takes him out. I did say next step is probably to get some advise from the vet.

I adopted a dog from Portugal, another history in itself, but did consider a greyhound.
The Asso I contacted recommended enrolling them in sports for dogs. I imagine there are more greyhound clubs in the UK than here (in a deserted mountain region in France!). Also that they do have diet problems...
I raw feed my dogs, and they thrive on it. I get a variety of meats, tripes etc. Frozen. I cook up frozen veg and mash it. I make 2 days supply at a time.
Maybe a change of diet, with, so I have been told, pumpkin in it. Meant to help with tender tummies.
It's quite a thing finding the best diet and lifestyle for an adopted adult. Especially those who were not well treated before.
Good luck to your DD, I'm sure with time it will sort out.