My mother is all day asking where is her husband. She has no memory of this going on. My father is in denial about my mother's illness. And as for me, no one asked me to look after both. I sound selfish. But this with my mom I am so angry inside :( it’s all day 24/ 7 . Even nurses get a break . Tell me how someone is to stay positive in this situation.
You say you are so angry inside because of your mom's repeated asking about your father. Anger comes from an unmet expectation. Perhaps you still expect your mom to be her old self and she no longer is. Since you posted that she has dementia (and short-term memory impairment apparently), an important thing you can do for yourself (besides finding ways to get breaks) is to learn more about dementia and how to engage with people who have it so that your daily interactions can be less upsetting. I learned a lot from watching Teepa Snow videos on YouTube. She's an expert on dementia and works hard at uplifting caregiving and coming at solutions from a positive angle.
As far as your dad is concerned, if he is still mentally competent and you are not his DPoA maybe ask for a hospital social worker to meet with the both of you. This person can answer questions and help you navigate options regarding rehab, discharge and home care . I'm not that familiar with what Medicare will cover during and after rehab but others on this forum can shed light on that.
Do your parents have the financial means to pay the cost for some in-home aids from an agency to help with your mom? Even if it were a few hours every day, or overnight. If you are not currently DPoA for either parent, they still may be able to create this authority for you. The hospital will have the forms and also a notary. You don't need a lawyer to create this document, especially if there are no other siblings who may challenge the PoA. In fact, you may be able to get the DPoA for both of them (if you want it) at the hospital if you bring your mother along. Hospitals do this all the time.
If neither of them agree to give you DPoA, then you will definitely need to loop in social services to get them on their radar as vulnerable adults. It may turn out that the county attains guardianship of them so that they can manage their medical and financial affairs, apply for Medicaid, etc. You're not at this point yet. More info from you would be very helpful, like if PoA for either of them exists, and how old they are. I wish you much rest and help from the hospital as you move through this very difficult situation.