Structure is important to people with dementia and it sounds like this routine is part of the way she structures her day and it is important to her. Since there is a safety issue, it does not sound like it is safe for her to walk by herself, and as her dementia progresses she will be needing more and more help. Could someone walk with her? Is there a relative, friend or neighbor that could visit her and walk with her? Are there neighborhood groups or senior centers that she could join and walk with others? Would you be able to hire a caregiver to spend time with her and walk with her? Also, Care.com has Senior companion care services that could spend time with your mom and walk with her.