Hi. Welcome. I am a Licensed Master Social Worker with more than 20 years experience working with individuals and families on a variety of issues.
While I can't comment on the medication aspect of things, i can offer you support for what is going on.
i think you are on target that the anxiety and depression could be causing her increased pain.
It is so very hard for you because you live so far away and she refuses to do anything to help herself.
if your Dad is okay living like this with her and doesnt want to move closer or place her in assisted living then there might not be more that you could do other than to give him the emotional support when you need it and maybe make some schedule for you and your sister to take turns to go and spend a few days with them.
I see you are offline now, but I am here so when you come back on we can chat more.