My mother has moderate dementia. She refuses to even go to a doctor any longer and claims there is nothing wrong with her.

When dealing with the stubbornness that comes with cognitive impairment we start with trying to make whatever needs to be done fun. For instance a trip to the doctor is more fun if it starts with fun getting dressed music, followed by a trip to the zoo, and ends with lunch wherever he wants to go. A shower may be more fun in swimsuits and done together, if you have a big jacuzzi style bath then that's even better fun.
Next level is negotiation, and remembering that "truth is relative". Disable the television, explain matter of factly that the television only works if everyone in the room smells nice. Therefore everyone must shower or bathe before it will work again. Yes, that means you too.
Next level is one we seldom use because it's so negative but if Pops refuses something vital like the medication that stabilizes his mood we matter of factly tell him that if he refuses to take the meds that keep him from becoming violent I can't take care of him anymore and the doctors will have him put into a care home.
Make sure to communicate these plans with the doctor so you can get backup of what you are doing at doctor visits. When we had to force the meds issue with pops due to violence we made sure to get all the family, friends and docs on the same page so they were all telling him the same thing.
Remember that with cognitive impairment they may not remember what you said 5 minutes after you said it so you will have to tell them again and again and again. Good luck.

You may need to call Adult Protective Services (APS) and report an adult at risk. Tell them she has dementia and is refusing your help. Say you are afraid she will get hurt, or worse. APS has branch agencies that can help her. It’s not all about abuse and neglect with them.