Assisting with dental care such as brushing with a person who has dementia can be quite challenging. The first thing to consider is to keep the person functioning at a high a level as they can. If your mom can brush her teeth on her own, let her do it. Stay by her to make sure she does do thorough brushing. If she needs assistance, you may brush her teeth.
You mention that she also has a dry mouth. An older adult loses their thirst mechanism that tells their brain they need a drink. Without the thirst mechanism, an older adult may easily become dehydrated. It is vital to offer her a drink frequently. Dry mouth can also be caused by certain medications such as antidepressants. Keeping hard candy around goes a long way to help with dry mouth.