Hello, I have a 3 year old dog I rescued a 5 months ago. She is fully housetrained - she has never peed or pooped in the house. I do not have a fenced-in back yard (getting a fence is not allowable per landlord). There is a dog park (15 minute drive away from home) that I can take her to on most days. But on the days I can't take her to the dog park, she holds it. She has held it up to 4 days in a row.

Here is what I have tried (including on that 4 day stretch where we couldn't go to the dog park: Taking her out on a 25 foot leash, tying her up in the privacy of the backyard for 30 minutes, and leaving her with her 1.5 year old adopted sister and I sat on a lawn chair nearby (facing away from her and reading a book) (no luck)
Taking her out on the 25 foot leash, tying her up in the backyard for 30 minutes with her sister, and I went inside. No luck.
Taking her outside without her sister on the 25 foot leash, tied her to a tree for 30 minutes, and sat facing away from her. Still no luck
Taking her outside, tying her to a tree, and went inside for 30 minutes. Still no luck.
I have also tried holding the end of the leash and looking the other way, so being tied to a tree or being held by a human - it doesn't matter - she wont poop.

I was finally able to take her to the dog park on day 4, and she dumped 6 loads.

I have also tried walking her around the dog park on the 25 foot leash in the hopes she will go. Still no luck. Every time she poops, she gets a treat.
At the dog park, if I say "go poop", and if she has to go, she will poop. So, she knows what "poop" means. But, she won't go on the leash. Oh, and her 1.5 year old sister has no problem pooping in the back yard, and 4 other neighborhood dogs all poop in the yard, so it probably smells like a toilet to all the dogs except my stubborn 3 year old.

Oh, and I have taken her to the vet, and the vet says some dogs are just very stubborn (really?!?). and, she received a clean bill of health.

Does anyone have any ideas?