We’ve been fortunate enough to have older housetrained dogs with our last couple of puppies (personal pets - not rescue dogs); that and a dog door. The puppies just learn from the older dogs. A good friend of mine used the same sort of method with her JRT, with great success.
We crate trained all of our rescue dogs immediately (from puppies to 6 year old adults) and I have to say that is the most successful method I’ve ever used. It sounds like you are doing what you can, maybe Kryswyn can offer some advice. All of the JRT’s I know (owned by horse people or not) have issues with being “told” what to do! One friend’s JRT uses the pillow on her bed as a toilet…when she’s really mad at her owner, she will poop right on her feet (usually when my friend is sitting down to dinner, watching tv and not paying attention)…the dog is a twit! So just know that you are not alone - and hang in there!
There is no crying in baseball!!!