This exercise (from J. Donnoghue's Inner Empathy) is suggested not for use with children directly, but rather to grow/heal one's ability for giving "unconditional love", thereby enhancing connection with children:
Are you willing to go back to a time and context when this part (bk: i think this refers to the part that is judgmental/with-holding) was active, try and recall as many details as possible and experientially connect with the part, i.e. emotionally connect with the part?
This part that wants to love in a conditional way, are you willing to welcome it? Can you stay with that part that wants to love conditionally and allow the feelings? Can you ask it what it wants you to know?
Are you noticing strong feelings or judgements about the part that wants to love conditionally, that could be another part emerging and wanting to be heard. Are you willing to check in with this 'new' part and see what it is feeling and needing, what judgements it holds?