Dogs can and DO FREEZE to DEATH. There are cases of police dogs (GSD) with long fur left in a kennel (with a dog house) and being found frozen to death. And you can IMAGINE the "howl" - literal & figural - of both the Animal Cruelty folks and the general TAX PAYERS - whose money PAID for the trained police dog who was lost - for no good reason, except negligence. In your case, you have a short coated dog, who is NOT used to living outside full time so it is not acclimated to cold weather nor does it have the insulating long or even DOUBLE coat FOR it. Your neighbors could report you (plural) for leaving the dog outside once temps dip into the thirties and you PLURAL could be charged with ANIMAL ABUSE (which has now been pushed into being a FELONY CHARGE). Ask Dad & Bro if they want to FACE animal abuse charges & an automatic felony?
I am SURE some accommodations can be made to divide and carefully share the house so no dog is loose at the same time, or in the same area. IMO the ****-zu needs to be MUZZLED when around your dog or ought to be on-lead & PREVENTED from BITING.
I would BET, BRO doesn't let that nasty biting behavior occur at the vet's office - or he would be SUED (by the bitten dog's owner) & might be told by the vet, never to return for any further service!!!!!!!!!!!! I agree, his dog NEEDS to learn some decent dog manners before he bites one too many dogs & it is the LAST THING...... he ever does.