Sorry to hear about your troubles. I would suggest the crate or a pen when you can't keep a direct eye on him. In terms of him being crated while the other dogs are loose, they don't really associate that with "I'm bad" or "that's not fair."
I have an 11yr old mix breed who's great indoors and when we aren't home and only uses her crate for a bed. She rarely is closed in it. We also recently adopted a Chihuahua from the pound. He's been living in kennels for almost 8 months, so he needed a house training refresher. I kept him tethered to me (6ft leash attached to him and my belt loop) whenever I was home and just puttering around the house for the first week or so. Any time I can't keep an eye on him he goes in his pen.
He doesn't associate it with bad things, he's actually quite happy to go in, even though the other dog is loose. Basically he's either in my sight or in his pen at all times. As he gets better I get to be less vigilant with him. I noticed it helping a lot.
A daily walk - even if it's a half hour, or in the evening will definitely help as well. I feel you on the cold thing, it regularly gets -40 here in the winter. A walk stimulates them mentally more than just running in the yard would. If it's too cold though, maybe chasing a ball or playing with him indoors for a while would help release some energy for now, until it's nicer and you can start getting a daily walk in with him. Again, it doesn't HAVE to be in the morning. An evening walk is still better than no walk
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