One of the brothers is a Muslim already alhumdulillah, but the mother of his young daughter isn`t. I wish there is tips you are able to offer because he told her about Islam already but maybe he didn`t have the right approach.
Jazakom ALLAH khair
wassalamo alikom wa rahmato ALLAH wa barakatoh
All praise be to Allah, and may His peace and blessings be on the greatest messenger, Muhammad.
In principle, we do not advise inter-religious marriages, and that is for several reasons, but since they are already married, then he should be kind and fair to his wife, for dawah is mainly through conduct and behavior and less through statements and arguments.
Moreover, here are some tips for him to use:
1- Be righteous himself.
2- Take his wife to masjids that cater to non-Muslims, and where there are pleasant, knowledgeable and eloquent sisters that she may associate with.
3- He may delegate to her taking their daughter to the masjid and different Islamic activities.
4- He should have patience and not lose hope.
5- He should learn about his religion, to be effective in his dawah, and to be balanced and moderate in his practice. This will, hopefully, help her see the beauty of the religion.
6- He should not compromise the religion for her, for she will not value his religion if he, himself, does not value it.
May Allah guide all to his way.
Allah knows best.