Can I take my granchild who is 4 to the doctor while I am baby sitting her?

If it's an emergency, go to the ER.

Does the mother know you plan to take the child to a doctor? What problem does the child have?

can i take my granchild who is 4 to the doctor while i am baby sitting her?

There isn't enough information here to answer you properly. Why do you feel the need to take your grandchild to the doctor?

I have legal paperwork which gives me parental permission and consent to have my step-grandchildren medically treated when they are in my care.

Doesn't answer this question, of course, but can block future problems.