Thank you for your query at DoctorSpring.com.
I understand your concern and admit that this is quite a difficult situation.
If she has recent onset slurred speech, and right upper limb weakness, a stroke is very likely.
In this scenario, she definitely needs urgent medical attention. Calling the paramedics is what you can do.
You can read the rest of my reply later.
As long as she is mentally capable, forcing her to accept medical care is difficult.
If she has dementia, and is found to be incapable of making sound healthcare decisions for herself, you are entitled to take healthcare decisions in her best interest and according to what she would have wished.
I know it can be very frustrating and difficult but if she is not mentally incapacitated, it is always better to talk to her to explore her reasons for refusal of care. Ask questions to determine why she is refusing help -- then you can tailor a solution. The reason could be about a lack of privacy, fears about the cost of care, losing independence or having a stranger in the house / living with strangers. If you have the resources, you can even hire a geriatrics counselor for this as they are able to create a relationship and dialogue with her / his clients. That person can also be your sounding board on which way to go. According to what your grandmother's reasons are, you can explore suitable options like having home care or transfer to an assisted living facility. If resources are limited, then ask the hospital social worker for a referral to the right agency in your area that handles social services and aging issues for seniors
Another option is to ask your County's Commission on Aging (Area on Aging in some counties). There are also free Senior Legal services available in some counties. And Senior Centers often have a Social Worker on staff, or an attorney who does free consultations.
For now, it is best to call the paramedics and get her the much needed medical attention. This may or may not result in her hospitalization depending on her mental status and whether her wishes can be considered or not.
If she is hospitalized, then it is easier to get her into a facility. It allows you to draw on the resources that exist there--discharge planners and social workers who can help convince your grandmother that she needs help and assistance or advise you on the best way forwards.
In summary, don't hesitate to ask for help. And don't worry you're doing a good job of looking after her in the best possible way.
I hope this was helpful. Let me know if I can assist you any further.