If my 96 year old mother is in the hospital with pleural effusion and atrial fibrillation, is that enough to refuse to take her home?

Sounds like you moved into her home temporarily to help care for your Mom. Tell the hospital social worker that you are returning to your home and will not be there to care for your Mom upon her discharge. They will need to arrange for STR or LTC as her condition warrants. Hopefully someone (you or a friend) has the necessary paperwork (DPOA, advanced directive) in place. However, if tests reveal that she can manage safely at home the hospital will release her-- and of course she can always sign out against medical advice and call a cab particularly if there is not a dementia diagnosis.
If you can get her into a facility for STR , traditional medicare will pay for the first 20 days provided she is participating in rehab and progressing. If she is in a facility for skilled nursing, traditional Medicare will pay for the first 20 days that she continues to need skilled nursing. After 20 days traditional Medicare will pay 80% of continued needs up to 100 days. The remaining 20% is paid our of your Mom's private funds or her supplemental insurance if she has that. Medicare Advantage plans have different guidelines so you would have to check that policy. Medicare (and Medicare Advantage) is a health insurance and will not pay for long term care (LTC). Medicaid is the insurance that pays for long term care and you or your Mom will have to apply for that. Medicaid is different in each state but generally you have to spend down assets to about $2000. This usually includes the sale of Mom's biggest asset, her house, to pay for her care in a facility.

Once you get the hospital to get her to a facility, I suggest you quickly find a certified elder care attorney who specializes in Medicaid to give you specific guidance.
Good luck!!

Can you keep her safe at home? If no, you need to talk to the hospital social worker and say that very adamantly. Safe is a trigger word that they must respond to.

Maybe tell them you'll sue. You are not bringing her home.

“I can’t possibly do that.”

Repeat it to yourself, then to them.

You’ll be both saving yourself, then your Mom.

Ask for the hospital SW, then repeat it to that person.

My mother had pleural effusion seven years ago. She's never been anywhere near the same since. She was on oxygen at night for several months (generated by a noisy machine), had to be helped to the bathroom to avoid tripping on 50 feet of oxygen tubing, and developed heart failure and vascular dementia.

My dad insisted on caring for her at home and never would have considered putting her into LTC, but in reality, within about two exhausting years, she probably should have been placed. I stayed with them and helped the first month, as there was no way my dad could have done it alone. She eventually got off the oxygen, but nothing else improved. The pleural effusion continued, too, and she had to be drained three more times over the next eight months.

I can't see doing this alone for a 96-year-old.

Don't bring her home.

This morning she has become combative, refuses all her medication and is demanding to go home. The nurse is telling me I may have to come get her because they won't be able to keep her. Because she owns her house and I moved in with her they said they will have to let her go home and I will be there to care for her. I barely had time to get a little sleep, so I haven't been able to get moved out yet, I was hoping the hospital could buy me more time. She doesn't understand that she has destroyed my life, I had to put my life on hold, give up my job and my apartment to come live with her because she refused to go to assisted living. Now I'm stuck, there's no way out. I was hoping the hospital would keep her at least 3 days, but then they would have to keep her for the weekend and they aren't willing to do that.

You can speak with the social worker about placement

You cannot both refuse to care for your Mom and care for your Mom, no. Living in her home may not become problematic dependent on what you two have set up. Are you her POA? It is too late with a diagnosis of dementia to set up POA in most instances, but honestly may be crucial if you are to act for her, assist her by paying bills and etc. Be careful not to comingle your money now.
If your Mom is diagnosed with dementia but deemed well enough to return home, what are your reasons for not wanting her to do so? If you feel you cannot care for your Mother then you may need to make that clear to the Social Worker or Case Manager involved, and ask for a clear diagnosis and placement for her. You may need to see an elder care attorney to discuss what you have in place or what you can put in place to get her assistance with bill paying and etc.

Request a cognitive/psychological exam TODAY, while she is still hospitalized.

Tell them you will not take her home unless testing indicates she can safely manage on her own.

Speak to the social worker where she is hospitalized and explain that you cannot continue to be her caregiver. Do you hold her POA? If so, how soon can you sell the house? Do you have your own residence available?

Say No, say NO, say NO.