Are you talking about a doctor or dentist (as in the title)???
Basically, whichever it is, the answer is the same. Yes they both can remove you from their list and make a space for someone who lives in the area.
The best thing to do is just say you still live at your mum's. At least you do have a family member at that address so it is not completely false information.
As long as you are willing to travel there to appointments. Bear in mind that for a doctor, you will not get a home visit out of the area.