Something I'm worried about, is will they want to try to hold me responsible for her state
They may investigate if there are signs of abuse or neglect, similar to child protective services. An unresolved UTI is not a sign of abuse or neglect, particularly since you got her to the hospital for it, and you've been in and out of the hospital with her for a variety of other recorded reasons.
If she has specific types of bruises or broken bones they will certainly investigate, if she has significant untreated bed sores they will investigate, and there are likely a number of other things that might point towards abuse or neglect.
They will similarly open an investigation if someone requests they do so or provides other evidence of abuse or neglect.
In other words, you will probably not be held liable for her illness(es) and/or dementia. It's common in the elderly, and not a sign of abuse or neglect. It's possible that they will ask you a series of questions about her care, but you might not notice because they've been doing this as part of her intake procedures every time you visit the hospital. They ask a number of questions to detect abuse, and on examinations the physicians also look for signs of abuse. They don't talk about it openly or tell you, and chances are you've simply gotten used to the questions and rattle off the answers without thinking about it.
I doubt you are in any danger of an investigation, and you can safely put that thought out of your mind and focus on the next step for her. This is going to be rough enough without worrying about whether you'll be blamed for something.