Stop dodging — I want you to answer my question.

Literal

Dodge don't-[ないで], my question [to-に] answer [want-て欲しい] [explanation-んです].

はぐらかす ('to dodge, to evade (a question)') is a verb specifically for verbal evasion — changing the subject, deflecting, giving non-answers. ~ないで attached as a negative request 'don't do X.' ~て欲しい is the structure for 'I want [someone] to do X': [verb-て] + 欲しい (i-adjective 'wanting'), where the other person is marked with に. んです again provides the explanatory/plaintive undertone — the speaker wants to clarify why they're insisting.