At 12, Casey may have some aches and pains and her hearing and eye sight may not be as good. I can understand your worried and you may have to make that decision, so no you aren't wrong to feel the way you do. A bite would be horrible for your young daughter and I'm sure that is what you are worried about. Before doing that I would take her in and have a full vet exam, check bloodwork maybe, but have her joints etc checked. If she is painful, many meds out there may help and without the pain she may be more tolerant. The slight growl is a warning that she has enough and would like to be left alone.It was good to separate them, since it can escalate, but Casey was just trying to say please leave me alone. Also if you try to keep her longer, talk to your daughter about how to pet Casey and when to leave her alone. She is young, but with repetition can probably learn when you say enough, she needs to leave Casey alone. If she has a lot of anxiety and it is causing problems, there are some meds you can talk to your vet about. I'm not advocating unnecessary meds, but for severe anxiety some make a difference in some dogs.
Growing up we had a golden, and I was older when she reached the age where she starting having old age issues. She did have arthritis and using an NSAID gave her many more pain free years and kept her comfortable. By the time she was 16 she would sometimes snap if she was asleep and you touched her without talking and making sure she saw you first. She never tried to get near you with her mouth and was just startled and surprised. No one put her at fault and we just made sure we talked loud enough she could hear us and did not touch her hip area as she was waking up, since she could get stiff.
Good luck to you in the coming weeks as you make a very difficult decision and I hope you have a wonderful vet that can help you make sure there is nothing that could be causing some of the problems and also to make the final decision.