I know nothing about pack of dogs and behaviour but your getting great help here from what I read. I just wanted to add something I noticed. It appears to me the trouble started with dogcare - its possible Luke learned this behaviour there - maybe has had to adopt this attitude to get by in his day with other pushy dogs. I realize regardless of where/why it started it must be dealt with, but perhaps daycare is not the best environment now. Is there a home with one other dog he can go to or would having a petsitter come in work better, till you get back to where you were.
I can imagine how this puts you are pins and needles. If I get a little puppy nip, I am reacting for a bit pulling my hands away faster than normal. This must be nerve wracking for you and your sister but keep working on it.