Luki is a beautiful name for a beautiful boy!
I am so so glad he is doing a little better - I think that is an excellent sign! I'm really hoping he gets a little better with each day and I hope the other pup that is at the vet is going ok too but you need to focus on Luki - the other family are obviously animal lovers who want to do the right thing too and have other resources if they can't cover the costs.
Years ago I used to volunteer to clean, feed and socialise the puppies at the big RSPCA shelter in Brisbane. They had this special clear chemical that we would put on the floors when cleaning and also in these shallow dishes outside every door of every run. Every time we stepped in and out of the runs we would put our shoes in the shallow dish to avoid spreading germs. And I remember back then we put garlic powder and other assorted supplements on their food too which I think helped. Anyway once I got home my boots stayed outside for a scrub and my clothes came straight off and were washed seperately. I never wore those boots of clothes for any other purpose either. I never took anything home to my dogs and yes, saw sick pups and ugly poos every single time I went to there as the pups for rehoming and incoming pups were caged along the same run. You'd know who wasn't going to make it when you saw one wearing a black tag.
But none of that for Luki - he has a comfy bed and a new mummy who just loves him to pieces already. How could he miss out on that!