Welcome, and I'm sorry she's having problems. I have a special place in my heart for minpins, they are special dogs, they are just different from other dogs somehow. I love that little prance that some of them do.
Yes, there is hope, especially when she still has the ability to urinate on her own. There is something called conservative management, where you treat the dog with medication and rest and see if the disk will gradually heal itself, and if it is not too bad often it does heal itself. They say it takes 6 weeks for a disk to heal, but they recommend 8 weeks of strict rest to ensure it heals fully. I was told by someone on Dodgerslist that they actually prefer 10 weeks because they have seen less recurrence that way. I am not a vet but I think the 8-10 weeks of strict rest is especially important for cervical disks because it is harder to rest them. With a disk in the back, you can crate the dog and prevent him from moving. But with a disk in the neck, even when she is crated she is going to move her head a certain amount, so you really want to be sure she gets the rest she needs.
I am sorry for being longwinded about this, but it's important, so please forgive me...
Conservative treatment means strict crate rest, in the crate 24/7, only out of potty. It requires tough love, you can't get soft hearted and feel sorry for the dog and take them out to play. Carry the dog out to the potty location and carry her back. She should do no more walking than is absolutely necessary to do her business, no stairs, no sitting on laps, no sleeping in bed, no lying next to other pets (unless she is on the inside of her wire crate and the other pet is on the outside, in that case they can lie next to each other), no lying on the sofa while the family watches TV, just very
strict in every way. Kids need to be told the dog is off limits right now.
For added motivation to do strict crate rest, it helps to think about the consequences, especially with a neck problem. If you have a dog with a disk problem in the back and it gets worse, the result is a dog who can't use his hind legs and is incontinent. He might need a wheelchair, but he can still have a happy life. If you have a disk problem in the neck that gets worse, in the worst case scenario you have a dog screaming in pain on the examining table and your only choices are immediate surgery or euthanasia. If a disk in the neck ruptures, the dog loses not just the use of the hind legs, but also the front legs, and it affects everything from the neck down, including the muscles that control breathing, so you really can't afford to take chances with a neck problem.
It is hard for the owner to have to be so strict, and for so long. If you started now, you would be going till about the end of January. Sometimes when the dog starts feeling better, the owner lets them out. Or someone in the family starts to feel sorry for the dog and thinks a little break won't hurt. But they say you can't do that, you need to go the whole time, because if it's not fully healed you will have a setback and undo all the healing.
I liked what you said about using blankets to support her. It may also help to raise her food and water bowl if you didn't already. It might also help if you develop a system with her where you let her know you are going to pick her up. For example, reach for her and say "Up-up-up" or whatever words you choose, so she is prepared for you to lift her. If you think about it, every time you lift her it will affect her neck, but if she knows you are going to do it she can maybe kind of brace herself. There was one family with a website of a chihuahua with neck problems, and for a while the owner found she could not even carry the dog, but the dog did OK being carried in a basket. I'm not sure what the difference was, but the dog liked it better.
The prednisone should help. There was a Yorkie here named Dukie who had cervical problems and he was on a low dose of prednisone for months, but they did get him through it. If you think she is tense in her neck and shoulders you might ask the vet about muscle relaxers. Also, if she is cold natured, you might consider turning up the heat in the room where you have her crate. That way you might help her avoid tensing up from being cold, and maybe keep her from using her head to burrow under her blankets.
You might want to read the literature on Dodgerslist, http://www.dodgerslist.com
. As for the situation of not doing surgery, from the way it sounds I do not think I would rush into surgery anyway, unless she developed unmanageable pain, which hopefully will not happen with strict rest. She's 13 and she still has bladder control and is not in excruciating pain. I think if it was my dog, I would try the conservative treatment and give it the best shot I can. If surgery becomes unavoidable and you want to do it, there is an organization called Care Credit that gives loans for emergency veterinary care. http://www.carecredit.com
. Oftentimes the vet hospital will have the application at their reception desk, and you find out right away if you are approved. The terms are good and you pay it off over time.
I hope something in this post helps. She sounds pretty good, considering. If you can get her through it, you may have to make some lifestyle changes, such as no jumping off the couch or going up and down stairs, and no playing with the other dogs if you think they might jar her neck again. But you'll have 2 months to think about that. I hope with rest and TLC you can have her feeling better soon.