This sounds so difficult, but I agree with the other posters here that it would help if you let go of some of your expectations of how you wish you were being treated. You don’t have any control over your family members, but you do have control over yourself. Be nice, only give things that you can give freely, without expectations of what you’d like to see in return.
The dog argument saddens me. Was the dog sick? There are ways to help someone care for their dog without offering an ultimatum that includes them getting rid of the dog, which was not up to you. I’m sure this just alienated your daughter-in-law, and I feel like we are missing part of the story because yes, a restraining order is pretty extreme.
When you were in the hospital, if she stole from you, try to see that as a lesson that she can’t be trusted. That doesn’t mean you can’t be warm and friendly towards her, which might help repair the relationship. Make some friends who you can trust.
Don’t give your granddaughter expensive gifts. Don’t try to tell your son how to parent. Just be kind and playful with your granddaughter, only with cheap and simple toys. If her father sees her enjoying playtime with you, it will hopefully inspire him to want to play, but either way, she will enjoy her time with you more if she doesn’t have to choose between you and her parents. Did you play with your son when he was young? If not, let him know how you regret that, and how you would like to have a better relationship now. The tension between you and her parents is pushing her away because it makes her uncomfortable. They can’t turn her against you, only you can do that.
Try letting them know that you are sorry for not respecting their boundaries, and would like to start fresh. Focus on just being a good friend and grandparent (occasional phone calls, small gifts, friendly letters, whatever they will accept, ASK THEM) , and let them live their lives. Hopefully once you back off, they will come around and be nicer to you. DO NOT, I repeat, DO NOT, ever tell them how you helped your parents.