"To resolve this dilemma" means to find a solution or make a decision that can solve the problem or conflict that is causing uncertainty or difficulty. Full definition
Otherwise, the therapist may rush to resolve the dilemma by aligning against the targeted parent, thus, allowing for a shared — albeit false — reality with the child. (parentalalienationsupport.com)
I should have resolved this dilemma in the public interest and not in the interests of my privacy. (politics.co.uk)
Some in despair may seek assisted suicide: simply saying this is wrong doesn't resolve their dilemma or relieve their distress. (faith.org.uk)