Can my mother's doctor drop her as a patient if we don't agree to a DNR?

The physician can indeed “drop” her if his ideas for her best care conflict with what she wants or what you direct, if you are her agent and your authority has kicked in. This is not as painful as it sounds, however, since the physician will be obligated to first find or refer your mother to a doctor willing to carry out her wishes.

Finally, since the doctor seems to be relying on you to make decisions about your mother’s care, it is likely your mother has become unable to express her own wishes. You need only be sure that refusing the DNR is what your mother would want. If that’s the case, be prepared to fight for her rights.