I'm not much help on the separation anxiety, but wanted to weigh in and say thank you for what you are doing to help. Every little bit is GREAT!!
Two of our current dogs are rescues - one of whom followed our daughter home...well sort of. Though we tried to find her owners - no such luck and she fit in so well that eventually we've had her spayed and she is now a member of our household. She's a cutie!! and has received some basic training in manners and advanced training our daughter's way in other things... Our daughter moved into her own place and took her dog with her - only to find that she had severe separation anxiety w/o the other people in the family, no outside area and no other dogs. The whining, crying and howling almost got Sierra booted out of her apartment. She brought her home in tears (we are only about 45 minutes drive away, but at the time sierra was working full time and going to ITT part time and the apartment was literally 5 minutes from where she worked and 15 from ITT). In some ways it was great for us - I love the little sneaky pooch. BUT she's a hole digger and right now we can't put her out in the back yard with the boys because we can't find her latest escape. So she's in the house and then out on the tie line out front - bleck - she's a "tree wrapper"... O well. We still end up with the 2 much bigger boys settled between hubby and I and then 1 or the other of us has Chicka on our laps until her person arrives home (O, forgot to mention that after a year of living on her own, she simply became overwhelmed with the cost and living on her own and moved back in w/ us) - at which time she vacates (& leaves nail holes in our bodies as we become living spring boards) our laps and leaps into Sierra's arms - all 35 lbs of her pretty, long red haired self w/ the soulful eyes!
The 2nd dog is one that our oldest daughter, before she moved out, got from a neighbor who refuses to spay/neuter any dogs and always has from between 10 to 30 dogs about 1/2 mile from us back in the trees... Gobbles came to us as a puppy, named Goblin as he was born Halloween week and was black and white... Part pit, part something and part dalmatian (so they say), he's developed a lot of the size and breadth of a pitt. When oldest moved out - she's never been in a situation to take him with - so he's always been with Larry and I. Will have to dig out records as I have no idea how old he is now (yet I can remember at least the birth years of each of our 37 head of horses and ponies, go figure) - think 4 or 5 right now. He, too, has been neutered. Nothing really problematic with him. Just a big smoochy love bug! He drools some (especially if you are eating dinner in front of the tv), he snores and OMG - the farts can drive you out of the room... But he's our Gobbles.
On the other question, which I know that the OP has both had answered and pretty much answered for herself, we found another dog a few years back. At the time, we stuck up flyers w/ pictures we took and some of the info on the dog (he'd arrived with a collar, had been cared for, was pretty "cool" but was all male - pitt we thought but not entirely sure). Put an ad on Craig's list. Our daughter also took him to two separate vet clinics in two different towns and counties (we live between them), contacted the Animal Shelters in both counties. He wasn't micro-chipped and no-one had seen him and no one knew who he was. I was pretty upset when our daughter, who seemingly knew better, let this unknown dog into her bedroom and onto her bed! All I could think of was what if he's sick, has rabies, is mean, attacks if she talks in her sleep etc, etc... He, too, was a great big love bug and I gradually relaxed somewhat. Honestly, he was beautiful! But he was HUGE and his mouth would easily wrap around my thigh (I'm not small). Right from the start, he was Skye's dog and if someone came too close to her (even her boyfriend at the time - which warmed me right up to him,
), he'd growl and "ruff up". That wasn't completely acceptable (UHHH = MY HOUSE), but we worked it out. I think it lasted three weeks, when suddenly Skye called me in tears. Someone had seen one of the flyers and knew someone who knew someone... Owner called Skye. I wasn't there when the owner arrived - but even Skye had to admit that it was his owner. The dog responded right away to "his name" (different than what we'd been calling him - which he'd started to respond to), tried to get to his owner while on leash, wrestled with his owner (a young man that ended up in tears according to Skye's boyfriend whom thought that was totally un-manly! still ROFLMBO when I think of this...). The owner confirmed it quit nicely when he had us call his vet clinic more than 50 miles away and they were able to tell us about a couple of scars (I knew one of the vets from the clinic, so was pretty sure it wasn't a hoax) on the dog - but were surprised that we hadn't found the micro-chip (he'd been chipped) or his rabies tab (well the hanger had been on his collar originally)... So the dog went home w/ his owner. He lived more than 18 miles away and had the dog in a fenced back yard and sometimes chained when he wasn't home (at work or?). Said there was a running feud between himself and some of the neighbors and felt that someone had let the dog loose and maybe even transported him part way to somewhere else (?), but wasn't sure. He had flyers similar to ours - but in his area. Quite the surprise to find that out!! Of course, we knew he was an unaltered male - but turned out he was a show dog and had done well as a younger puppy but hadn't been shown recently. He was 2 years old at the time we found him. He did know lots more than we thought - but with different terms and his name turned out to be "Jack". It was after that that we ended up with "Gobbles"...
We kept in touch for a while, but haven't heard from him lately.
Anyhoo, just wanted to share our experiences! Again, I bow to you - rescuing a dog that you can't really keep... Explained in depth in another post...