I am under the impression that once you ask an adult child if you can do their parent's temple work and they say know you are not supposed to ask another for permission. Is this correct?
That is correct if one close family menber refuses permission then permission is not given and further action should be curtailed until after the 110 year rule no longer applies. In addition, if family is opposed we are to respect their wishes and do nothing to cause friction. The following article describes when you need permission but your question falls into the last paragraph