​💔 My children want a relationship with their half-sibling, but the Mother won't allow it

My children had a close relationship with their younger half-sibling (about five years old) until my ex-partner (the father of all the children) broke up with the half-sibling's mother. Since the breakup, the half-sibling's mother has completely blocked communication and contact. ​My kids deeply miss their sibling and are very eager to resume a relationship

​I am not sure how to proceed.

​Tell my kids there is nothing I can do and try to help them move on?

Or

​Continue to try to establish contact with the mother on behalf of my children