I'd be tempted to leave him at the cousins... so far you've taken him out of the house that he's used to and popped him in a kennel (some dogs just don't kennel well) shoved an electric collar on him which has hurt - I'm surprised he still trusts you after doing that albeit for the best of intentions.
One thing you can do is pop a radio on sometimes they like a little comfort and familiar noise, make sure he's warm dogs like greyhounds and whipets feel the cold more than other because of their lack of coat. Start reading up on separation anxiety.
I don't think you've read the whole thread, yes I took him out of the house to a kennel (with his best mate) he then came BACK INTO the house with his best mate and was still the same, even whining sat on the sofa with the family, the collar had only been charged for 2 hours, I tryed it myself on low and high, and also popped it on to my other dog Lexi and she barked without it affecting her at all, fully charged I wouldn't even go there with Binx,
he's not cold they have heatlamps in both kennels, and also coats, that's the first thing I bought when looking into pure whippets, separation anxiety happens when a dog is stressed when he's away from the family/or one member of it, Binx is still the same when ALL the family are sitting down to watch TV and he's whining over the TV volume, lying on the sofa, and if it was that, my cousin would have had a nightmare with him, but he's been fine there,
I'm begining to think it's me, I'm to soft, I talk to him and fuss him when he starts to whine, and when he howls I'm still giving him attention by telling him no or giving him treats to shut him up for a bit while he's eating them, I did ignore him though for a whole day, but he continued until midnight, I couldn't take it anymore and gave him a pig's ear to chew for a bit of quiet, (which lasted an hour) all the dogs also have loads of chew toys, balls, rope toys, in there runs with them,
Chance my bitch to whom I've had the longest and who I have bonded with the most, I haven't heard a peep out of her, nor none of the other 3, it's just Binx, this is the big part I don't understand