If the girl decides to dissolve her marriage, she has no respite in the mosque.
She has to approach court of law with a petition under section 2 of Dissolution of Muslim marriage act, 1939 for filing a divorce case against him.
In that event your brother will receive summons from court. He should not ignore the summons.
On receipt of summons he should appear before court, give his counter or written statement denying the allegations made by her in the divorce petition and object her reasons for filing this petition by stating that she approached the court with unclean hands.
There is no reason for letting it go exparte against him if he appears and contests the case.
If at all she wants to settle it in an amicable manner, she may be advised to comply to the demand of return of mahar and all your gifts with her.
There is no reason to compromise with her without she obliging for this condition.
No doubt your brother cannot force her to come and live with him though he can manage to obtain a judgement in his favor advising her to join him in the matrimonial life and resume cohabitation or conjugal relationship, if she is not willing to do so, hence it is better to discard her relationship at this stage itself, however your brother should not become a fool in their views to dance to their tunes, he has to concentrate and enforce his rights for compensation towards the fiscal and mental loss he suffered.