George, I am so sorry you are going through these issues.
A proper euthanasia (in my opinion) should be a two part process. The first is a sedative to calm the cat. Either a shot or gas. Some vets, like the one who put down my Lily, don't do the sedative and thus cat can become quite agitated while an IV is inserted for the barbiturate that will stop the breathing and the heart.
Some vets may inject the barbiturate directly into the heart. I don't know anything about this, but Stefani (and Toonces) has told me it is an inappropriate way to euthanize. In fact, Stefani is my "go-to person" on euthanasia. You might want to PM her.
As for preserving remains, I haven't heard about the bag either and I think any restrictions against burying animal remains with human remains would be a matter of state law, and you should consult with a mortician (or two) in your area. I have been reading a book by Robin Cook called Intervention. One of the story lines has to to with a search for the ossuary box holding the remains of Mary (mother of Jesus). I had to look up what an ossuary is.
Here's the wiki page. I will be brief, as to not upset someone reading the thread, but it involves a proces of burying the remains and then after some years, removing the skeletal remains and placing them in (what would be the case with you cat) a sealed box that could then be buried with you. I am not sure that I could personally handle that process with one of my cats, but perhaps you can talk with a pet cemetery in your area about this and other options.
(((((George)))))