That is a lot of stress all at once. I think anyone would be feeling it to some degree or another. Have you used any coping skills or spent any time on self care today? Sometimes a distraction can help pass the time and give you an outlet for some of the built up pressure.
As far as the job goes, do your best to prep and then try to relax about it as best you can. Keep in mind that they are also interviewing with you. They are trying to assess if you are a fit for the job, but you also get to see if it is a fit for you. If it isn't and you think it would cause more stress you can walk away. You haven't invested a ton in this opportunity yet. If it is a good fit then you can pursue it further. If not, then you have a job already.
Do you have a reason to believe you will lose your current job? Go in and focus and give it your best every day. That's all you can do.
I am sorry to hear about your father. I know it can be difficult to deal with a mentally ill parent. I have been there. It is especially difficult when you have to consider your own stability as well. If your Dad were well he would probably insist on you taking good care of yourself.
You're not whining. You came here for a kind ear and support. I hope you are able to find what you need. You're on the right track getting it out. Sometimes talking things through can ease the weight enough to make things bearable again.