Welcome to Talking Point and I hope you find lots of support from everyone here.
I am sorry that you are having this sort of experience but unfortunately with dementia patients your story is a very common one.
Many carers are accused of all sorts of things from having affairs to stealing money, keys, personal belongings, hiding anything and everything, lying, conspiring with family members and on it goes.
Paranoia seems to be part and parcel of many of these diseases and there is no one answer for your problem. I think that when it occurs, it is best not to let on that it is upsetting you. Keep calm, try and change the subject and overtime, you will hopefully develop a thick skin.
I hope that others will be along soon, perhaps with some better ideas.